# Vedantu JEE Made easy - Limits L-2 ｜ Class 11 Maths Chapter 13 ｜ JEE Maths

Add to Playlist

Report

Vedantu

## Category

📚

Learning###### Transcript

00:00:00Hello everybody, good evening, good evening my army, kya meri sari ki sari army yaha pe

00:00:12pahun chuki hai because I am super duper excited for limits part 2, yes, so in case aapne limits

00:00:20part 1 miss kar diya hai jahaan pe actually we build upon the entire concept to jaake zarur

00:00:28revise karna, so limit 1, jo limit part 1 tha, lesson 1 tha uske andar we discussed

00:00:35what is exactly a limit through visualization, uske baad we discussed some methods, ab aaj

00:00:43hai baari aage aur methods ko build upon karne ki and of course to play quiz, toh yaar har

00:00:50method samjhane ke baad mere paas bahot saare questions hone wale hai, kya meri army ready

00:00:56hai, yes or no in the chat box, yes bachon sab ke sab tayyaar hai ki nahi super awesome

00:01:03session ke liye, bilkul, toh chalo start karte hain, usse pehle yaar this is the schedule

00:01:08we are following for the week, toh if you are 11th yaar 12th ka student who is preparing

00:01:15for school exams for JEE or NDA then 5pm is the time jahaan pe chal rahe hain humare concept

00:01:23building sessions, so for class 12th the days are Monday, Wednesday, Friday and for

00:01:30class 11th humare din hai Tuesday, Thursday, Saturday, so part 1, part 2 and part 3 exclusively

00:01:38humne rakha hai for indeterminate form which is your Lopital rule, wo sab discuss karenge

00:01:43detail me ki kis kis form par wo laga sakte hain, but aaj kya hone wala hai, its going

00:01:50to be super super amazing, lekin aage jaane se pehle aapko bata de ki 1 rupee can actually

00:01:57fetch you a lot of knowledge, so aap kya kar sakte ho, aap issi video ke neeche yaar, ek

00:02:05link hai for your micro course, matlak ki jab aap iss video ke neeche pohanchte ho,

00:02:14so you would find this, micro course at just rupee 1 and yes it is just for rupee 1, so

00:02:20pehle aap apna grade select karte ho, lets say grade 11, then you can select any of these

00:02:27subjects, lets say math I select, now you can see yaha pe bohot saari cheezein hain

00:02:34aapke liye, for example you want to do sequences and series, when you click on this, ab yaar

00:02:39ek rupee ka matlak yeh nahi hai ki ek chota sa session, no, ek rupee ka matlak hai that

00:02:45you are going to learn sequences and series, ab dekh sakte ho yaha kitne sessions hain,

00:02:50so yeh saare sessions ka aapko access mil jayega, yes, so basically micro naam se micro hai,

00:02:58iska price probably 1 rupee hai, but it actually gets you, gives you access to a lot of material

00:03:04and recorded session ke saath saath, if you want you can even opt for the live sessions,

00:03:11theeke, to yaha se aap live courses pe click karke, upcoming live sessions ke liye bhi,

00:03:16khud ko aware, I mean khud ko actually, what do you say, enroll kar sakte ho, theeke ji,

00:03:23everybody, absolutely, right, and bachcho agar aap JEE 2020 ke candidate ho, toh aapko pata

00:03:30hai, keeping in mind that it's going to be held in July, July 18th to 23rd ke beech

00:03:37mein, so you know we are, basically this is the time ki aakhri month hai, toh ismein bilkul

00:03:43aapki do or die situation hai iss waqt, jitna padha hai, usko revise karna effectively bahut

00:03:49zyada important hai, and we do understand, and isliye we have launched a brand new batch

00:03:58for your JEE 2020 which starts on 15th of this month, yaani ke basically sabse pehle

00:04:06jaise hi aap enroll karte ho, aapko ek poora iss tarah ka schedule mil jayega, okay, toh

00:04:11kab kab kya kya aap revise kar sakte ho, humare saath live, right, so har roz aapki 3 to 5

00:04:17hours ki live classes hoti hain, physics ki, mystery, math ki, toh yaar yeh bahut hi detail

00:04:22mein aapko, yaha main aapko 1st of June ka sample dikha rahi hu, jaise aaj dekho, aapki

00:04:274pm pe gravitation hui, 6.30 thermodynamics, 9pm binomial, so aapko pata hai revision kis

00:04:34tarah hone wali hai, right, so entire month we've got you covered, ismein aapki testing

00:04:40hone wali hai, so 10 plus aapke test hone wali hai, jisko aap analyze karoge, and suppose

00:04:46yeh chapter complete hua, let's say binomial aapka complete hua, aapko uske notes mil gaye,

00:04:53aap uska jo bhi aapne live session dekha tha uski recording kabhi bhi dekh sakte ho, and

00:04:58the best part is bachcho, you get access to the content library once you enroll for the

00:05:03course, and yaha yaar content library pe jab aap click karte ho, so you get access to the

00:05:10most important questions which you should be doing right now, toh jaise agar main aap

00:05:16binomial theorem ki baat karu, so for instance yeh dekhiye, aapko notes mil rahe hain, and

00:05:22uske saath saath aapko most important questions from this chapter mil rahe hain, yeh dekhiye,

00:05:28right, and this happens for all physics, chemistry, math, so if you're interested, isse video

00:05:33ke neeche jaake, this is what we have bachcho, vdnt.in slash jeecce, aur yeh main kyun bata

00:05:42rahi ho, kyunki humaipas ab bahot kam seats rahe gaye hain, yes, if you click on buy now

00:05:47and apply my code nagcc, okay, nagcc, toh aapko yeh course ka special price hai, which

00:06:00is an added benefit, 3999, yaani ki 4000 rupay mein aap physics, chemistry, math teen ho revise

00:06:06kar sakte ho, and it's not about the price right now guys, it's about ki aap kitni effectively

00:06:11is one month ko use kar sakte ho, alright, everybody, chaliye, start karte hain fir issi

00:06:18ke saath, humara aaj ka one of the very important topics, so aaj ke video mein what all topics

00:06:25are we going to cover, standard limits, jispe mein abhi aa rahi hoon, then we are going

00:06:30to discuss exponential limits and we are going to discuss logarithmic limits, inn teen limits

00:06:37ke around we are discussing a lot of questions, so I hope each one of you is ready, jo jo

00:06:42yahaan pahun chuka hai usne video ko like kar diya hai, channel ko subscribe karke rakh

00:06:47liya hai, alright, so this is the first set bachho, jo hum discuss karne wale hain, okay,

00:06:55so ab iska pattern pehchano, okay, I am not getting into the proofs of any of them, wo

00:07:02hum log of course binomial se kar sakte hain, jab situation aayegi we will see if it is

00:07:07needed, aap yaha pe dekho dhyan do, kis tarah se isko karna hai, x raised to power n, minus

00:07:16a raised to power n, and neeche yahi x and yahi a copied hai, but your limit is going

00:07:22from x tending to a, agar ye situation hai, pattern ko bahut dhyan se observe karo, you

00:07:29have limit x tending to a, base mein x minus a hai, upar x minus a hai, lekin yaha pe n

00:07:37hai, ab ye n kya kya ho sakta hai, n should be positive, n should be a positive integer,

00:07:43ya phir even if it's a rational number, us case mein a has to be greater than 0, toh

00:07:50in cheezon ko bahut dhyan se yaad rakhna, kyunki it appears very simple, lekin condition

00:07:56gadbar nahi honi chahiye, okay, so yaha pe the answer comes ye jo power hai, into ye

00:08:03jo constant term hai aapki, n minus 1, isko dhyan se note kar lo, bahut important cheez

00:08:10hai, which is going to help us further, for instance phir se batario, yaha x and y mein

00:08:16confusion nahi honi chahiye, it is only a symbol, so if I say let x, limit x tending

00:08:22to heart bolu mein, toh aap samajh jao x raise to power n, minus heart raise to power n,

00:08:31x minus heart, toh ye symbol hai, ye teeno same hone chahiye, yes, ye teeno same hone

00:08:37chahiye, the final answer becomes bachchon, heart raise to power n, minus 1, and of course

00:08:44ye power aayegi, bahut derivative se milta jilda lagta hai, jo hum start karenge next

00:08:49week, this is going to be the final answer, alright, ab ek cheez samajh lo, proof iska

00:08:55yaar binomial ke through kar sakte hain, toh jab hum binomial theorem padhenge, then we'll

00:08:59discuss it, right now, just please make a note of this, iski saari conditions yaad kar

00:09:06lo, ab aapka quiz time ho gaya, toh har concept samjhate hi aapke saamne questions aayenge,

00:09:13and I'll be giving you 30 seconds, toh timer chalne wala hai 30 seconds ka, aapko answer

00:09:19apply karna hai, sab pehle mujhe bata do, ek baar likh liya hai aapne ye formula, yes,

00:09:23have you written it, sirf formula likh ke rakh lo, kyunki aapko help hone wali hai, everybody

00:09:28chalne aage, chalye, so let's begin with the first question, very very basic, yes bachcho,

00:09:50very very basic, I think most of you have answered, most of you have answered, alright,

00:10:06I think mostly bachcho ne answer kar diya hai, unhone form dekh liya, dekho A ke baare

00:10:11me kuchh nahi diya hua, so we're assuming, waise bhi agar yaha aapka N, agar aapka N

00:10:19hai, yes bachcho, if this is already a positive integer, toh aapne kuchh dhyan nahi dena,

00:10:24bas ye cheez dekh lo, kya ye teen ho same hai, extending to A, yaha bhi A, yaha bhi A, so

00:10:304A cube, kitne bachcho ko ye mil gaya hai, I know kahi bachcho bolenge, bohati basic

00:10:35answer tha, but hum dheere dheere build upon kar rahe hain, kis kis ko mil gaya hai, ek

00:10:39baar hi likh do, ek baar thumbs up dikha do mujhe in the chat box, so then I can quickly

00:10:43move to the second question, yes bilkul mil gaya, very very easy, theek hai chaliye, let's

00:10:50move to the next question on your screens, let's see isse kitne bachche answer karte

00:11:11hai, I want to see the correct answer yaha pe, okay, time's up, time's up, and bohat

00:11:28saare bachcho ne yaha par jawab diya, they attempted and I can see a lot of you are correct

00:11:34also, theek hai isko dhyan se dekhna, what are we going to do for this, just realize

00:11:40yaar aapki form thi, limit x tending to a, x raise to power n, minus a raise to power

00:11:46n, upon x minus a, yaha pe ulta hai, yes it's the other way round, to isko same karne kiliye,

00:11:54I can divide up and down with x minus 1, main upar neeche x minus 1 ke saath divide kar

00:12:00sakti hoon, so what will I get, limit x tending to 1, this will be 1, upon x raise to power

00:12:071 by 4 minus 1, and this is x minus 1, ab main 1 ko yaar 1 raise to power 4 bhi likh

00:12:12sakti hoon, ab main ek baat kari thi, one condition, ki yaar yeh agar aapka rational

00:12:19number ho jaye, even if it's a rational number to chalega, even if it's a rational number

00:12:25to chalega, but a should be greater than 0, jo yaha pe hai, to condition ko dekhna bohot

00:12:31zaruri hai, is it getting satisfied or no, to ab yaar upar to 1 hi hai, yaha kya ho jayega,

00:12:371 by 4, 1 raise to power, jo bhi 1 by 4 minus 1, ab yaha pe answer 1 by 4 aagaya, to 1 upon

00:12:451 by 4, yaani 4 was the answer, kitne bachon ko 4 mil chuka hai, everybody in the chat

00:12:51box, yes, everybody in the chat box, kisi ne mujh se poocha, ma'am what if the powers

00:12:58are different, matlab aapne bola, jaise x raise to power n minus x raise to power m

00:13:04hai, sorry, x raise to power n and yeh hai, yes, aap directly formula nahi laga sakte,

00:13:12then you cannot apply the direct formula, ab aapko yaar to issi form mein lana padega

00:13:16yaar kuch aur karna padega, so understand these powers should be the same, they cannot

00:13:21be different, tabhi baar baar aapko dhyan dilwaya tha, ussi condition pe, I understood,

00:13:27are we ready for the next one, kyunki iska toh answer mujhe mil chuka hai, 4, yes, let's

00:13:33take the next one, ok, let's see this one, yes, it's for ISC students also, let's see

00:13:53isko kitne bachche karte hain, ok, time's up, time's up and I can see a lot of correct

00:14:11answers jo bachche yahan pe de rahe hain, theek hai, so I will make you, I will make

00:14:16you understand bilkul, keeping in mind jo hamara standard tha form, our standard form

00:14:24was this, x raise to power n minus a raise to power n upon x minus a, theek hai, basic

00:14:31basic sawalo se we will keep going higher, abhi bahot saare methods learn karne hain

00:14:36aaj, so yaar yeh x minus 1 hai, but of course I can divide both sides, I mean I can divide

00:14:43up and down with x minus 1, aise kar sakti hoon main and you know limit gets split, limit

00:14:51agar yeh poore quotient pe wo split ho jati hai, yeh cheez hamne lesson 1 mein padhi thi,

00:14:56correct, so what will I get, cheeke ji, ab yahan pe of course I can write it as 1 raise

00:15:04to power 15, this as 1 raise to power 10, toh directly what can I get making use of

00:15:09formula 15 into 1 raise to power 14, hai na, and this one is going to be 10 into 1

00:15:15raise to power 9, my answer is 3 by 2, mujhe pata hai agar you are giving, yeh koi step

00:15:21aa jata hai kisi competitive level mein, toh directly yeh answer aa jayega, hai na, and

00:15:26x tends to 1, toh directly 3 by 2, kitne bachon ko samajh aage hai 3 by 2, ek baari I should

00:15:33see this smiley in the chat box, so that I can go aage, everyone, come on bachon, yes

00:15:43guys, absolutely great, toh chalo aage badte hain and let's understand the next one, isko

00:15:50solution toh 3 by 2 hot chuka hai, here's the next one, let's see this, come on, come

00:16:14on guys, let's do this, ok, I can see a lot of you have answered and bohot saare correct

00:16:31answers mujhe aaj chat mein dikh rahe hain, which is amazing, theke toh isko kaise karenge

00:16:36zarar samajhte hain, everybody, yaha pe you cannot see the form directly anywhere, theke

00:16:42kahin form humko nazar nahi aari, but ek cheez humko nazar aari hai, which is this,

00:16:473, hai na, 3 ko I can always split as 1, 1, 1, bilkul theek, so yaar kya milega mujhe,

00:16:57this is going to be x, and main yaar isko dekho 1, 1, 1 karke, main kisme believe karti

00:17:03hoon ki main sabko baat dungi yeh 1, so I'm gonna give 1 to x, I'm gonna give 1 to this

00:17:10x square and we are going to give this 1 to x cube also, ab isko bhi separate kar do,

00:17:17let's separate them aao gachon, cheeke ji, so limit applied to all of them, yeh toh yaar

00:17:24pehle hi 1 ho raha hai, this is already 1, toh mujhe kuch nahi karna, this one yaar toh

00:17:30main wo formula lagao, yaar main directly factorise kar do, I can write this as x-1,

00:17:36toh x-1 cancel ho jayega, yaha pe 1 plus 1, 2 aa jayega, and for the last one bachon,

00:17:43I can apply jo limit abhi abhi seekhi hai humne, which is this, yes guys, which is this,

00:17:49toh yeh kya ho jayega, plus 3 into 1 square, yaani ki 1 plus 2 plus 3, which is 6,

00:17:57kitne bachon ko 6 mil gaya hai, firse bolungi yaar, aapme se ho sakta hai,

00:18:02toh bahot bachay soch rahe hoon LH rule lagane ke liye, LH rule is not allowed in a lot of

00:18:07schools, theke toh school ka exam de rahe hoon, toh definitely, but haan LH rule ke

00:18:12bhi apne restrictions hai, kaha lagta hai, kaha nahi lagta, wo sab discuss karenge on

00:18:18Saturday, where we have the next class, abhi yeh sabko samajh aagaya, yes, yes or no in

00:18:24the chat box, everybody, everybody, yes, amazing yaar, bahot awesome kar rahe hoon

00:18:33tum log, seriously bachon, seriously, chale toh iska solution mujhe mil chuka hai, which

00:18:39is 6, let's go ahead and kill the next question, are we excited, lekin usse pehle, I want to

00:18:45see some likes on the video right now, taaki I get the feedback, ki mere bachon ko yaar

00:18:50aise sessions aur chahiye, bilkul chaliye, let's go aage, this is the next question,

00:18:56okay, let's see, isme kitne bache correct answer dete hain, let's see, yes, yes, yes,

00:19:25okay, okay, time's up bachon, time's up, toh I can see a lot of responses, which are 3,

00:19:34kya 3 correct hai, is 3 the correct answer, yes, yaar kuch missing hai yaha pe, socho

00:19:42zara bachon, 3 correct answer hai, yaar kuch missing hai, ab kuch bache plus minus 3 hai,

00:19:49ek Pralad neko dikh raha hai, ek Manisha ka naam dikha hai yaha pe, Jagriti, yes, now

00:19:53understand this, sabse pehle toh yaar aapko yeh standard form dik gayi, toh aapne likh

00:19:57diya 5A raised to power 4 is 405, A raised to power 4 is 81 and yaha se bohot saare bachon

00:20:05ne mujhe answer 3 de diya, kyu beta minus 3 nahi dal sakte idhar, I can put minus 3

00:20:12hai na, yeh, this is an even power, so plus minus 3 is the answer, agar aapne 3 diya hai,

00:20:19agar aapne 3 diya hai, so your answer is incomplete, correct, this should be the exact answer,

00:20:25everybody, I hope sabko yeh cheez samajh mein aari hai, yes guys, I hope you are understanding

00:20:32this, yes, thank you so much Tisha, yes bachon, halwa hai, awesome guys, dekho halwa mein

00:20:39bhi kahi bachon ne galti kari hain, khali 3 de diya answer jaldi jaldi mein, ok, are

00:20:44we excited for the next one, yes, are we excited for the next one, toh dheere dheere

00:20:48hum build upon kar rahe hain and naye naye methods aaj seekhenge, a lot of tools you

00:20:53need to have for whether you are preparing for school exam, whether you are preparing

00:20:58for your JEE or your NDA, theek hai, chaliye, next one bachon ne bol diya hai, here it is,

00:21:04soch ke guys, yes, let's see, let's see bachon, isko kaun answer karta hai?

00:21:30Ok, time's up, time's up, time's up, yeh thoda sa teda tha question, thoda sa teda

00:21:43tha, so I would like to see ki kitne bachon ne actually isko correct kiya hai, theek hai,

00:21:48if you visualize this, sabse phere toh ek baat samjho, your standard thing says limit

00:21:56to a, x raised to power n, minus a raised to power n upon x minus a, aur hai yaar mujhe

00:22:02ek cheez bata de na, jab hum log, dekho part 1 ho gaya hai, part 2 ho gaya hai, lesson

00:22:073 mein hum log LH rule padhenge, uske baad agar aapko next week sabse phere test chahiye,

00:22:12before we start with derivatives, theek hai, test karna jab aapke paas mixed questions

00:22:19aah, that's the main challenge, acha ab yeh suno, this is what I have guys, yaha pe dekho

00:22:25yeh aur yeh different hai, this and this they are different, toh mein directly toh nahi

00:22:31laga sakti formula, I cannot apply the formula directly, kuch teda meda karein yaha pe, watch

00:22:37this out, kya yaar mein yeh toh chalo x plus 2 hai, hai na, this is also a plus 2, can

00:22:46I create, dhyaan se sunna, can I create x plus 2 and a plus 2 here also, x plus 2 and

00:22:53a plus 2 yes, baad bachche unhe likhna shuru kar diya hai, plus and minus 2, bilkul cheet,

00:22:58toh yaha pe agar main yeh kaam karu, x plus 2 minus a plus 2, kya hua hai yaha pe, main

00:23:04yeh add and subtract 2 kar diya hai, absolutely I have added and subtracted 2, ab yaar limit

00:23:12bhi match karni chahiye, limit bhi bilkul x tending to a hai, toh match karni chahiye,

00:23:17toh bilkul yaar, agar mera x a ko tend kar raha hai, so if I say x plus 2, it will tend

00:23:22to a plus 2, hai na, saari ke saari humaari conditions ho chuki hai, set, now I can apply

00:23:29the formula directly, I can say yeh ho jayega, n into a, ab yeh a poora hai, into n minus

00:23:381, matlab 3 by 2 a plus 2 raise to power half, agar aapko yeh cheez samajh mein aagayi hai,

00:23:47toh ek merko bulb dikh jaana chahiye, which means yes ma'am, dimaag ka bulb jal chuka

00:23:53hai, everybody, yes, is it buffering, ok, let's see, alright bachon, yes, it's fine,

00:24:08it's fine, ya, agar aapko yeh samajh mein aagaya hai, toh yeh ek baar happy wala bulb

00:24:13bana do ki, haan ma'am, ekdum set ho chuka hai, and is video ke neeche comment zarur

00:24:18karna mujhe, ki yes ma'am, we want a test on limits next week or no, thik hai, aage

00:24:24badhne se pehle humein yaad toh hona chahiye ki hum theek se padh rahein ki nahi, bilkul,

00:24:29everybody, yes, chaliye, great, awesome, toh aage badhte hain and now let's come to exponential

00:24:36limits, yaha pe ab hum exponential limits ki baat karne wale hain, so the most used

00:24:41forms, thik hai, the most used forms mein aapko batane wale hu, which are going to be

00:24:46these two, sabse zyada aapka school exam hai, aapka JEE exam hai, aapka NDA exam hai, aur

00:24:52bhi forms hain kaafi, thik hai, so if the need be, mein definitely unpe bhi videos karungi,

00:24:57but yeh do sabse zyada important hai, actually agar aap dhyan se dekho guys, toh yeh ek hi

00:25:04form hai, there's only one form, which is this one, this happens to be the most important,

00:25:13thik hai, kya ho raha hai ismein, aap zyada pattern note karo firse, everybody watch this

00:25:18out carefully, limit x tending to 0, hai na, this a is a constant, ok, this a greater than

00:25:260 is a constant, a raise to power x minus 1 upon x, ismein aapka answer kya raha hai,

00:25:32log to the base e of a, base amesha e rahega, yes, if nothing is mentioned, it is considered

00:25:41to be base e only, and this, ab yaha pe pattern note karo zyada x, x, x tends to 0, and yaha

00:25:50pe minus 1 hai, samajh mein aaya, iska matlab, agar main yeh kaam kar doon, limit, I can

00:25:59say, a raise to power a tree minus 1 upon tree, thik hai, tree tends to 0, main dikhane

00:26:09ke koshish kar rahi hoon ki aapka koi bhi symbol ho sakta hai, any symbol is possible,

00:26:15in this case also the answer is log a, toh yaar teeno ped same hone chahiye, and the

00:26:22ped should tend to 0, in that case your answer is finally a, hai na, bache bol rahe hai,

00:26:28maam har baar yeh aap tree kyu bana dete ho, aapko tree se bohot zyada pyaar hai, absolutely,

00:26:33toh samajh aagaya, nahi log to the base tree nahi hoga beta, tree toh x hai, x mein answer

00:26:38nahi hai, answer is in terms of this a, yes, samajh mein aayi yeh cheez, absolutely, now

00:26:45just understand, iski jagah main e daal doon toh, iski jagah main e daal doon toh, its

00:26:52actually applying the same formula, but yeh ho jayega log e to the base e, and isliye directly

00:26:58answer 1 aa jata hai, its actually that you are remembering only this, samajh mein aaya,

00:27:05everyone, yes or no in the chat box, yes or no bachon, theek hai, chale aage, is everybody

00:27:15ready, ek baar isko, iska agar screen shot lena hai ya note karna hai toh kar lo, kyuki

00:27:20now I am starting with quiz on these questions, let's see, let's see, theek hai everybody,

00:27:27chalo, time to start with some quiz questions, think about it, aapki form kya thi, agar aapko

00:27:54clear nahi hai, a lot of questions we will do, it will be crystal clear to you, ok, so,

00:28:01ok, ok guys, ok, ab yaha pe na, dekho pehle, samjho yaha pe kya form thi aapki, form meri

00:28:11kya honi chahiye, limit extending to 0, a raise to power x minus 1 upon x is log a,

00:28:22kuch toh mujhe a raise to power yeh dikha, hai na, but there is no minus 1, there is

00:28:28no minus 1, toh main isko begin kaise karun, how do I begin with this, main plus minus

00:28:331 kar sakte hoon, itna haq toh banta hai mera, absolutely, so what can I do bachon, I can

00:28:42do plus minus 2, plus minus 1, yaha yaar main ne minus 1 kiya, and is taraf main ne

00:28:49plus 1 kiya, ke kya, minus 1 plus 1 kar diya, sabko ye cheez samjh mein aaye, and yaar isko

00:28:59alag kar diya, now one question had two hidden questions in it, yes, ek question mein do

00:29:09hidden question hai, ab aap yaha pe dekho abhi bhi directly nahi kar sakte, kaise, maam

00:29:14kyu nahi kar sakte, ab yaha dekho, this is 2x, but yeh toh x hai, this is only x, koi

00:29:21baat nahi, I can multiply divide with 2, hai na, I can multiply divide with 2, ab yaha

00:29:27aa jao, yeh toh 3 hai, 3x, koi baat nahi, I can multiply divide with 3, correct, yeh

00:29:34cheez sabko samjh mein aagayi, everybody, bohot saare bachche 1 dere answer which is

00:29:40wrong, dhyan se samjho, iska answer log a hota hai, matlab if I apply limit to the first

00:29:46one, yaar yeh mera 2 toh alag hai, 2 is separate, mera answer yeh aa jayega, log e to the base

00:29:543, hai na, kyu, kyu ki powers meri match kar gayi hai, yeh 2x ho gaya, yeh 2x ho gaya,

00:30:012x tends to 0, matlab of course 2x bhi tend to 0 hota hai, correct, toh yeh aa jayega

00:30:06mere paas, 2 log 3, yaha pe aao, this 3 is as it is guys, this 3 is as it is, yeh cheez

00:30:13dekho, yaha 3x aagaya hai, yaha 3x aagaya hai, so my answer is going to be log 2, ab

00:30:20zara, sabke sab bachche jump marenge in the chat box, I want to see jump, jump, jump,

00:30:26jump in the chat box, kyu, kyu ki yaha dekho yaar, aapko pata hai, yeh n log x aagaya hai,

00:30:33toh yeh jump marke upar paunch jata hai, correct, and same way yaha 3 aagaya hai, yeh jump marke

00:30:39upar paunch jata hai, basic properties of log, hai na, properties of log, toh yeh banjata

00:30:45hai, log 3 square minus log 2 cube, right, that means the answer is log 9 minus log 8,

00:30:57toh isko agar mai concise form mein likh doon toh log 9 by 8, yes, sabko yeh cheez samajh

00:31:06mein aagayi ki nahi, ek baari yes or no in the chat box, everybody, bohot saari jump

00:31:12hai, bohot saari jumps mujhe dikh rahi hai yaha pe, great, yes Anirudh, you can definitely

00:31:20follow these sessions to revise for your JEE 2020, if you want to actually polish your

00:31:26concepts, theek hai jee, sabko yeh cheez samajh mein aayi, hai na, toh question itne

00:31:31seedhe bhi nahi hunge, par aapko wo formula jo abhi bataya tha, wo yaad hona chahiye,

00:31:36theek hai, chalo, so yeh toh log 9 by 8 aagaya hai, now I am ready for the next question,

00:31:43kitne bache isme kya karte hain, aajao, let's see, let's see this one bachon, isko dekhte

00:32:08hai kitne bache karenge, thoda so aur sochna chahate ho, yes, ek baari timer ko aur chalaya

00:32:21jaye, thoda so aur sochon isme, ek baari timer dubaara, oops, sorry, haan jee, dubaara

00:32:28chalati ho ek baar timer, let's see, kitne bache isko kar rahe hain, kuch kuch toh bache

00:32:52jawab de rahe hain, but correct kitna hai yeh dekhna padega, okay, aap dekho, firse

00:33:01yaar dekho aapko constant raise to power x dekhta hai na, toh dimaag mein ek baar toh

00:33:06strike karta hai ki I can use that formula, hai na, I can use that formula, lekin wo formula

00:33:12apne paas pehle toh likhe rakh lo, ki formula was this, formula toh mera yaar yeh tha,

00:33:20and this is kahin se bhi yeh close nahi lag raha hai iske, aap socho kaise karenge, sabse

00:33:28pehle toh just focus on the numerator, yeh haan se yaar ek baar batao mujhe, 27 raise

00:33:34to power x ko I can write as 3 raise to power x, 9 raise to power x, hai na, can I do this,

00:33:46main 27 raise to power x ka yeh kaam kar sakti hoon, and 1-cos x kya hota hai, aapne

00:33:52trigon mere saath padhi hai, kitne bache ko yeh formula yaad hai, 1-cos x, what does

00:33:58that give us, it gives us 2 sin square x by 2, hai na, matlab yaar denominator ki toh

00:34:05alag hi story chal rahi hai, now just see this, kya ho raha hai yahaan pe, isko zarar factorise

00:34:11karo, kya factors bante hain humare, I can take 9 raise to power x common, toh 3x-1 and

00:34:209x-1, ek baar bata do sabko yeh factors mil gaye hain, yes, ek baar yeh bata do if everybody

00:34:29has got these factors, yes bachon, yes or no in the chat box, have we got this factor,

00:34:34yes, yeh dono factors mil gaye hain mujhe, aap mujhe kya chahiye, mujhe yeh x chahiye,

00:34:40this x is missing hai na, matlab mujhe yaha bhi x chahiye, mujhe yaha bhi x chahiye, aur

00:34:46ek mene lesson 1 me aapka formula kiya tha, kya tha wo, limit x tending to 0, yeh base

00:34:53ke liye, sin x by x is 1, lekin yaha pe sin square x hai, toh perfect hai, yaha bhi x

00:35:01chahiye, yaha bhi x chahiye, yaha x square chahiye, awesome, matlab numerator and denominator

00:35:07ko mai x square se divide kar sakti ho, yes, yeh cheez samajh mein aayi, pehle toh yeh dono

00:35:13formula dekh lo which I am going to use, these are the 2 formulae which I am going to use,

00:35:19theek hai, toh matlab mujhe upar bhi x into x chahiye, neeche bhi x square chahiye, toh

00:35:26awesome hai yaar, yeh toh set hai ekdum, theek hai jee, toh mai kya karungi ab, yaha

00:35:32pe yaar maine x se divide kiya, upar and neeche, yaha x se kiya and yaha doosre x se kiya,

00:35:39so x square ho gaya basically, and this one is going to be 2 sin square x by 2 upon x

00:35:46square, ab isme mujhe tension nahi leni, mera directly answer kya aa raha hai, log 3, everything

00:35:54is set, log 3 aa raha hai, yaha pe kya aa raha hai mera answer, log 9, theek hai yeh

00:36:00multiplication hai, usko please log a b mat kar dena, yeh log a into log b hai jo kuch

00:36:05nahi hota, it's log a into log b, ab neeche dekho, yaar neeche yeh kab poor hoga, yeh

00:36:11mai x square andar leke jaungi, toh I will have to multiply divide with 4, yeh baat kitno

00:36:16ko samajh aayi, ki we will have to multiply and divide with 4, ma'am aisa kyu karenge,

00:36:22yeh maine lesson 1 me bhi aise questions karwae the, aap basically kya karte ho, sin

00:36:28x by 2 hai, and basically if I take x inside, hai na, aise leke jaati ho inside, so I will

00:36:36have to, yaha bhi mujhe 2 chahiye, yaha bhi mujhe 2 chahiye, matlab if I take the square,

00:36:40mai square karun toh x square by 4 and 4 chahiye, theek hai, yeh humne part 1 me bhi pada tha,

00:36:47lesson 2 hai, lesson 1 jab humne trigo limits padhi thi, ok, so yeh cheez aapne kardi, toh

00:36:54aap mera answer base me kya aara hai, yeh 4 comes out bachon, yeh aapka 2 and 2 yaha

00:37:01cut chuka hai, yeh cheez 1 aagayi hai, cheek hai, I am left with 1 by 2, yaani mera final

00:37:07answer aagaya hai, 2 log 3 log 9, chaho toh yahin chhod do iss answer ko, everybody,

00:37:16ek baar hi isko dhyan se dekho, twice, ab isko yaar, upar chaho toh le jaa sakte ho,

00:37:23par inko mat combine karna, yes, everyone, yeh cheez samajh me aayi, everybody, toh

00:37:29kya kiya maine, yaha direct formula lagaya, yaha direct formula lagaya, that's why I

00:37:34am saying, saare session aapko revise karke aane, next session se pehle zaruri hai, kyunki

00:37:41yaar, next session me na pehle wale ka kuch na kuch use hota hai, correct, ho sakta hai,

00:37:47base me yaha dekhlo dubaara se, yes, dubaara se ek baar base dekhlo aapka, kyunki kuch

00:37:53bachon ko confusion ho raha hai, this is sin square x by 2 upon x square hai, aap aise

00:38:01bhi samajh sakte ho, sin x by 2 into x, sin x by 2 into x, aisa kyun kiya, kyunki whole

00:38:08thing hai, now I can multiply, divide with 2, chikay, toh yeh ho gaya 1, kyunki limit

00:38:15extending to 0 hai, yeh ho gaya 1, toh mere paas kya bach raha hai, 1 by 4, and 2 mera

00:38:20bahar tha, so 2 into 1 by 4, correct bachon, everybody, chikay, in questions ko yaar, dubaara

00:38:28se practice karna bohot zaruri hai, yeh ek baar me samajh aane wali, matlab aaj aati emotionally

00:38:34aur kuch ko time lagta hai, toh aapko dubaara se revise karna bohot zyada zaruri hai, ok,

00:38:39let's move to the next question, abhi toh beta bohot saare amazing questions aane wali hai,

00:38:44aapko end tak rehna hai tabhi, ok, next question on your screens,

00:39:05let's see, very similar, very very similar bachon, ok, ok, everybody, everybody, yeh

00:39:24ek baar hi aur agar dekhna chahate ho, chalo give it some more time, ek baar, ek baar dubaara

00:39:30se final answer dene ke liye socho isko, soch ke, aa, different different answer aare

00:39:48mere paas, let's see, yes, now I can see correct answers coming, yes, yes, bilkul,

00:40:02log 2 into log 5, bohot saare bache jawab dere hain, log 2 into log 5 and wahi answer

00:40:08hone wali hai aapka, ab dhyan se samjho kaise, ok, dhyan se samjho kaise, yahaan pe aapko

00:40:15pehle hi bol diya tha last question ki tarah karna hai, hai na, last question ki tarah

00:40:20karna hai, toh aapko samjh aagaya hoga ki aapke numerator ke yaar roots ban jayenge,

00:40:242 raised to power x minus 1, 5 raised to power x minus 1, yeh kitne bachon ko samjh aagaya

00:40:30ki mere root me these are the factors I am getting, yeh hum kar sakte hain 10 ko split

00:40:35karke 2 raised to power x, 5 raised to power x, bilkul previous question ki tarah, upon

00:40:41x tan x, upon x tan x, hai na, ab aapko yaar yaha bhi x chahiye, yaha bhi x chahiye, so

00:40:50and neeche, neeche mujhe limit extending to 0, tan x by x is 1, I will have to use, correct,

00:40:59correct, toh main kya kartiyon, main divide kartiyon yaar x square ke saath, let me divide

00:41:05with x square, toh yaha x, yaha x, yaha x square, perfect yaar, yahi toh chahiye tha

00:41:12mujhe, kyun, kyunki yaha se ek x apne aap pat jayega, toh yeh dekho, and x tends to 0

00:41:18hai, is cheez ka bhi dhyaan rakhna, this is log 2, hai na, this is log 5, and ismein koi

00:41:26tension nahi hui meri, kyunki limit extending to 0, tan x by x 1 hai, bas yahi answer tha,

00:41:31that's it, the question is done, the question is absolutely killed, and agar aapka yeh question

00:41:38ho gaya hai, toh ek baari chat box mein dik jana chahiye, KDS, yaani ki the question is

00:41:44killed, dead, slaughtered, everyone, just make a note of this, theek ke, bilkul, amazing,

00:41:52amazing, and yaar isi ke saath saath na, aap, make sure you are hitting that like button,

00:41:59ki motivation level stays up for me also, and mujhe pata chal jaye mere bachcho ko maza

00:42:04aa raha hai, yes, everyone, chaliye, let's check out, ab dekho aage jaane se pehle, very

00:42:14very important, firse bata rahi hu, agar aap J2020 ke candidate ho, then yeh ab aapka aakhri

00:42:22lap rah gaya hai, jill last one month, ya toh matlab jisse hota hai na, jaan laga do

00:42:28ya phir jaane do, and jaane nahi denge tumhe, samajh gaye, toh jaan toh lagaani padegi,

00:42:33and physics, chemistry, math, teeno mein lagaani padegi, waise toh I am coming up with a 30

00:42:38days strategy very soon, lekin, ek brand new batch start ho raha hai 15th of June se, kyu

00:42:45agar abhi tak bhi aapko nahi samajh aa raha hai yaar, revision kaise karo, dekho mai baar

00:42:50yeh bolti hu, ki crash course kyu zaruri hai, vidhantu ka nahi lena chahate, matlo, kyu

00:42:55zaruri hai, kyunki aapki padhaai ka level kuch bhi raha ho, ab tak, you have been absolutely

00:43:01exceptionally doing well, ya phir aapne bahut average tariqe ki padhaai ki hai, yeh aapka

00:43:07lap aa gaya hai, jissme aapne ab kya karna hai, revision karna hai, teeno subjects ka,

00:43:12and if you want to do it effectively, you can do that with us, yes, so 15th of June

00:43:18se batch start ho raha hai, limited seats hai bachu and yeh bahut popular demand pe

00:43:23start hua hai, so if you go to the, go to this link in the description and apply my

00:43:30code NAGCC, toh you are actually getting it at this slashed price, kyu slashed hai, kyunki

00:43:37ab yeh aakhri mahina hai and hum chahate hain maximum bachche humare saath judh kar faida

00:43:42uthain, and faida ka matlab yeh nahi hai ki mujhe koi faida hone waal hai, isme mujhe

00:43:47kuch nahi mil raha hai, right, isme agar mil raha hai kuch, toh wo aap logon ko mil raha

00:43:51hai, Vedantu ka yaar ek selfish motive hai, bilkul, wo main aapko bata rahi hu, hamara

00:43:56yeh motive hai, ki har bachcha padhe, jude, and effective revision kar sake, alright,

00:44:03chalein, alright, let's begin with logarithmic limits now, logarithmic limits ka pattern

00:44:11and then we will discuss a lot of questions, theek hai, this is what you have to remember,

00:44:16isme dekho dhyan se, ln ka matlab hi yeh hai that this is applicable when log is to the

00:44:24base e, yeh aapka exponential se bohot similar lagra hoga aapko, ln 1 plus x, yahan bhi x,

00:44:33yahan bhi x, ab bachche mujhe bolte hai, ma'am aap hamesha tree kyu lete ho, kuch aur lete

00:44:38dekhte hain aaj, samajh jao is pattern ko, ek toh log to the base e hoga, if it's not

00:44:44e, you cannot apply, 1 plus, 1 plus, yaar ek softy lelo, yes, ek softy lelo, aise nahi

00:44:54banti softy, aise banti hai, chalo jaise bhi softy khaate ho aap, aise lelo, upon the same

00:45:00softy and limit, this softy tends to 0, samajh gaye ho gaye aap, pattern ko zamjho, 1 plus

00:45:10jo bhi symbol hai, upar aur neeche same hai and it tends to 0, then your answer, koi meinat

00:45:16nahi karni, seeda 1 likh dena hai, theek hai, yeh sab main abhi aapko without proofs bata

00:45:21rahe hoon, theek hai, but of course if you want ki nahi ma'am inka saare proof ki bhi

00:45:26video bana do, toh we will discuss that separately, chalo mujhe bhi yaar aise softy ice cream

00:45:32bhej do, sab ke sab in the chat box, agar yeh cheez samajh aa gaye hai, yeh ek sample

00:45:36ke liye humne liya hai, ki koi bhi yahaan pe function ho, which function tends to 0,

00:45:41your answer is 1, yeh ek hi cheez hai, sirf humne different kuch karke dikhaya hai, all

00:45:47right, sab ke sab, samajh aaya yeh cheez humko, yes, everybody, theek hai ji, chaliye,

00:45:55are we ready for some dhamaka now, kya hum kuch dhamakedar questions ke liye ready hai,

00:46:01yes, I want to see some josh, hai na, neen toh nahi aagayi bachcho, jaldi se, I want

00:46:07some josh, kyuki now we have to get into action and solve a lot of questions, jaldi, jaldi,

00:46:13acha, cornetto bhej rahi ho mujhe, awesome yaar, meri favourite hai, awesome, chaliye,

00:46:18mai le leti hu camera se, tab tak aap ready ho jao for the questions here, all right,

00:46:23let's see, kya baat hai, kya baat hai, kya baat hai, kya baat hai, kya baat hai, kya

00:46:52baat hai, okay, time's up, time's up, yeh toh bachcho ne yaar, matlab question aate

00:46:59hi bola, ma'am 1, ma'am 1, 1, 1, 1 is the answer, absolutely, te dekho iske den humne

00:47:06kya kiya, yeh toh I'm sure sab ke liye by hand ka khel hai, and agar aap already left

00:47:11hander ho, toh aapke liye right hand ka khel hai, 1 plus, yaar yeh pattern, saari jagah

00:47:17same hai, and x tends to a bhi mirko batara hai ki x minus a tends to 0 hai, matlab yeh

00:47:23hai meri cornetto, samajh gaye, cornetto sabko dikh gaye yeh kya hai, agar aisa case hai

00:47:28log bhi natural hai, kyuki hum artificial me believe hi nahi karte hai, hum sirf natural

00:47:33cheezon me believe karte hai, the answer is 1, absolutely, bilkul yeh cheez sabko samajh

00:47:39me aagayi hai, are we excited for the next question, toh sabse pehle yeh ho chuka hai,

00:47:46time for the next one, let's see, yes alok it's absolutely useful for revising even for

00:48:072020 batch, ok, awesome, awesome, I can see a lot of correct answers in the chat box,

00:48:24matlab bachcho ko yeh pattern samajh aagaya hai, that's good to know, toh yaha pe dekho

00:48:30kya ho rahe hain, yaha pe aapka ek hi cheez nahi hai, yaha pe 2 different questions ko

00:48:35mix kar diya hai, samajh rahe ho, kya kiya hai humne, humko yaha bhi x chahiye, humko

00:48:41yaha bhi x chahiye, and x pehle se tend to 0 kar raha hai, toh yeh 1 aayega, yeh log

00:48:463 ho jayega, bahut bachche gadbad kar dete hain, isko bhi 1 likh dete hain, na na na,

00:48:51log a raise to power, sorry, a raise to power x minus 1 upon x, limit x tending to 0, log

00:48:57a hota hai, abhi humne discuss kiya tha, exponential limits mein, everybody, yeh cheez

00:49:02sabko samajh mein aagayi hai, everyone, chalo main aapko 3 seconds deri hoon, before I move

00:49:07to the next question, agar aap naye jude hoon is channel se, toh fata fat abhi ke abhi,

00:49:11wo laal wala chamakdaar button daba ke, channel ko subscribe kar lo, and video ko toh like

00:49:17karna banta hai boss, chalo, counting till 3, 1, 2, 2 and a half, yes, paune 3, chalo

00:49:263, alright, 3 ho chuka hai countdown, and let's move to the next question, let's see,

00:49:52aap mujhe pata hai, yaha confusion ho rahi hai bachon ko, answer toh dene shuru kar diye,

00:49:56but correct hai ya nahi, that is something you have to think about, aahaan, socho, socho,

00:50:03yahaan pe main batati hoon, bohot saare bachon ke answer, 1 aaya, log 10 aaya, the answers

00:50:10that you are giving me are 1 ya log 10, shravani, shravani ka answer bilkul correct hai, and

00:50:16aap toh bohot saare bachon correct de toh rahi hai yaar answer, aparna ka I think answer

00:50:22correct hai, aur yahaan kaun reshma dikh rahi hai mujhe answer correct hai, bilkul, ab aap

00:50:27isko dhyaan se socho, na iska answer 1 hai, na iska answer log 10 hai, iska answer hai

00:50:321 upon log 10, absolutely, now a lot of you are giving it correct, ab dhyaan se suno kaise,

00:50:39ye cheez kaise hoti hai, now listen to this carefully, ya maine ek cheez pehli batadi thi,

00:50:45isko 1 mat kar, isko 1 nahi kar sakte kyunki base 10 hai, and baby ko toh base pasand hai,

00:50:51kaunse wala base, natural base, kyunki we don't believe in artificial things, hai na,

00:50:57absolutely, toh mujhe yaar base change formula lagana padega, kaise aapko ye kaam karna

00:51:03padega, that's how we apply the base change formula, and ye x as it is aa gaya hai, ab

00:51:12cheeze set hai, kyunki yaar ye sab ka, sab 1 hai, toh 1 by log 10, ya natural log, ya

00:51:20log 10 to the base e, was the correct answer, yes everyone, accha kitne bachche hain, jino

00:51:27ne meri video dekhi hai, logs in one shot, aap logone bola tha, log ke properties ki

00:51:33ma'am ek alag se video bana do, how many of you have seen this video, yes or no in the

00:51:38chat box, zara dekhe, dekhe zara yaha pe, yes, everyone, yes, bahot saare bachchon ka

00:51:45yes bhi aa raha hai, lekin jisne nahi dekhi, sirf jaake youtube par aap ek naam type karna,

00:51:51log in one shot, and aap mera naam dal sakte ho waha pe, right, toh aap youtube kholna,

00:51:58chik hai, everybody, and yaha pe, bilkul ye cheeze dal dena, logs in one shot, chik hai,

00:52:11logs in one shot, agar channel pe nahi dhund sakte toh ye kaam kar lena, chik hai, ye aapki

00:52:17ek ghante ki video hai, but I, I mean, I can guarantee you, aapke saare concepts ko crystal

00:52:23clear kar degi, kahi bhi aap confusion hoti hai aapko, definitely watch this out, chik

00:52:29hai, definitely watch this out, jaise hi logs in one shot daloge, ye video pop ho jayegi

00:52:34aapke saamne, okay, okay, everyone, chaliye, let's go back to our question, ye wala question

00:52:41ka mere paas, jo humne aap thod diya hai, yes, 1 by log 10 answer aage hai, are we more

00:52:47excited for the next question now, maza aa rahe hain na, seekh bhi rahe hain, and saath

00:52:51saath quiz bhi khel rahe hain, this is the next question.

00:53:11Okay, a lot, a lot of you are giving me the answers, jinmein se maximum bache, I am so

00:53:32happy to know, maximum bachon ka answer correct hai, 1 by e dere hai bache answer, jo by the

00:53:38way ekdum correct hai, kaise kar sakte hain isko hum, dekho ek cheez mujhe samajh mein

00:53:43aagayi, one thing I am definitely understanding ki yaar yahaan kuch toh mujhe use karna hai,

00:53:50but ye log property use karne ke liye 1 plus x upon x chahiye, jo door door tak nahi hai

00:53:56humare paas, hai na, door door tak nahi hai, leke mai is 1 ko log e bol sakte hu, is 1

00:54:03ko I can call log e, aap dekho dhyaan se, limit x tending to e hai, log x minus log

00:54:09e ko yaar mai aise likh sakte hu, by properties of log, ye kya kiya maam, ye toh aapne bilkuli

00:54:15door bhej diya, bilkuli door bhej diya, na na na, meri form hai 1 plus, hai na, toh

00:54:21main 1 add or subtract kar leti hoon in the numerator, matlab I can do this, I can add

00:54:29x by e 1 and I can subtract 1, aap mai yaar isko ek term maan ke chal sakti hu, but ye

00:54:36same term meri niche bhi honi chahiye denominator mein, that means mai agar e common le loon

00:54:41I will be left with x by e minus 1, shabash, dekin ek abhi bhi kami hai, is my x tending

00:54:48to 0, ye jo maine banaya hai, kya ye tend to 0 kar raha hai, dekho zara, if I divide

00:54:57with e bachon, toh ye kya ho jayega, x by e tends to 1, yaani x by e minus 1 tends

00:55:03to 0, bilkul, toh yaar dekho firse bata rahi hoon, lagane se pehle, kya, thapad, nahi,

00:55:11lagane se pehle formula, you have to check for all the conditions carefully, ye, ye

00:55:17aur ye, teeno same hone chahiye and should tend to 0, theek hai, toh yaan se mujhe pata

00:55:23hai, everything is 1, yaar ye saara ka saara 1 hai, sirf 1 by e bach gaya hai, which is

00:55:31the answer, absolutely, absolutely, hai na, everybody, ye cheez sabko samajh mein aayi,

00:55:39yes or no, jaldi se, ek baari, matla agar ye humko samajh aa gayi, toh wahi wala bulb

00:55:46bana do yaar, happy wala bulb ki, haan maam, dimaag ki batti, tong, jal gayi hai, everybody,

00:55:52yes, yes in the chat box, theek hai jee, theek hai jee, sabko samajh mein aa gaya hai, ok,

00:56:04chaliye, amazing to see this, ab aajao beta, kitne bachche tayyaar hain for the next question,

00:56:10yahaan toh 1 by e aa gaya hai, and yaar ye notes ki tension mat le na, aapko pata hai,

00:56:14toh telegram group pe saare notes provide ho jate hain within 24 hours, alright, let's

00:56:20go, ab meri taraf se ek challenger question aa raha hai, challenger question aa raha hai,

00:56:26uske baad usko yaad karne ki, hanji, question ko yaad karne ki bhi trick bataungi, cheek

00:56:32hai, let's see,

00:57:02chalo, ab main kya chahati hoon, thoda sa aur sochon isko, theek hai, thoda sa aur sochon

00:57:10bachcho, oh oh, ek baar hi 30 seconds ke liye aur sochon, koi baat nahi answer dik bhi gaya

00:57:20hai, toh yaar samajh aana chahiye, toh baad bachche answer de rahe hain, I think aapne

00:57:36dekh liya hoga answer, yes, bilkul yaar, answer aapka 2 by 5 hai, cheek hai, toh aapko different

00:57:49different methods mil sakte hain yahaan pe isko solve karne ke, but main aapko batane

00:57:54wali hoon, the easiest, the quickest method, jiska answer aapko, I think sirf 3-4 lines

00:58:01mein aa jayega, cheek hai, full method bataungi jo aap school exam mein bhi kar sakte hoon,

00:58:07cheek hai, toh just understand, aur phir aapko wo pattern samjhaungi jisse answer aata hai,

00:58:12correct, let's understand this, dekho log ke liye firse wahi cheez, yaar yeh hona chahiye,

00:58:18mere paas, tab answer 1 aata hai, isko amesha likh lena side mein, taaki gadbad nahi ho,

00:58:26dimaag mein it's imprinted, cheek hai, yahaan pe sabse pehle if you apply property of log,

00:58:33firse bolungi, bohot tariqe hain iss question ko karne ki, I am going ahead with the quickest,

00:58:38log A-log B, if base is not given, toh hum E maan ki chalte hain, this is going to be

00:58:44log A by B, arey maam firse aapne wahi kaam kar diya, yahaan toh door-door tak mujhe nahi dikh raha hai yeh formula,

00:58:55can I not add and subtract 1 from my side, hai na, add and subtract kar lete hain 1 ko,

00:59:03kya ho jayega yahaan pe, 1 plus yeh cheez and minus 1 also, cheek hai ji, isko ek term bana do,

00:59:14kya aayegi mere paas, yeh kya term aa rahi hai, dhyaan se dekho isko,

00:59:18bachchu if I take my LCM, this is going to give me, 5 plus x minus 5 plus x, toh yahaan aayega 2x upon 5 minus x,

00:59:32maam yeh neeche toh hai hi nahi, yeh toh sirf x hai, yeh toh sirf x hai main isko kaise karun,

00:59:38yes, dhyaan se suno, main yahaan 2 upon 5 minus x se multiply divide kar doon toh,

00:59:49yeh kaam kar sakti hoon main, yes or no, yes or no, yeh kaam kar sakti hoon main kya kiya main 2,

00:59:55kyun kyun ki mujhe yeh chahiye yaar, yeh cheez chahiye, 2x mere paas sirf x hai,

01:00:01main 2 upon 5 minus x se multiply divide kar diya, bilkul samajh mein aagaya,

01:00:07ab yeh cheez dekh lo yaar ki kya yeh 10 to 0 karega, itna bada pahad,

01:00:12bilkul yaar x tends to 0 hai, toh 2x upon 5 minus x bhi 10 to 0 karega,

01:00:18hai na, toh ab mere paas kya aagaya, I have got this thing to be 1,

01:00:23par lab iski limit mila lo toh yeh 1 ban gaya hai, correct, yeh 1 ban chuka hai,

01:00:28and ab baaki mein yeh limit extending to 0 laga lo kya ban gaya mere paas,

01:00:345 upon 2, yaani answer is 2 by 5, the quickest method to crack this question,

01:00:41yes, the quickest method to crack this question, ab pattern samajh lo yaar yeh kya pattern hai,

01:00:47jab aapke paas limit extending to 0, log of a plus x minus log of a minus x upon x aajaye,

01:00:59toh aapka answer amesha 2 by a aata hai, yes you can generalize this also,

01:01:04but of course aapke school exam mein aayega toh method dikhana padega poora,

01:01:09aapko bohot quick wale method se sikha diya hai, but koi bhi positive constant aapko mil jaye,

01:01:15a plus x, a minus x, neeche x and limit x tends to 0,

01:01:19pattern do teen baar dekh le na samajh aajayega, answer uska 2 upon a hota hai,

01:01:24yaha 5 tha toh answer 2 by 5 tha, ya me 10 kar do toh mera answer 2 by 10 ho jayega,

01:01:30which is 1 by 5, samajh aagaya ki nahi, yes, aagaya ki nahi, jaldi batao mujhe,

01:01:37integration bhi start hoga Raji, thoda sa intazaar aapko karna padega,

01:01:42everyone ye cheez samajh mein aagaye, aap dekho mein aage bhi jaungi,

01:01:48aur aapko aage bhi bataungi, lekin usse pehle you have to do this,

01:01:51kahi bachche mujhe likhte hai mama kyu baar baar like like like kehte rete hai,

01:01:55bete jab aap logon ke liye mehnat hoti hai, these are all absolutely free classes for you,

01:02:01so the only gurudakshina we expect from you is, ki agar aapko genuinely maza aa raha hai,

01:02:07force aapko koi kar nahi sakta, genuinely maza aa raha hai,

01:02:10toh then when you hit the like button, it's like a positive feedback,

01:02:14ki mujhe bhi feeling hoti hai, haan yaar aaj bachcho ne kuch seekha,

01:02:18chalo ab ek kaam aap karo, socho socho yeh homework kaise karoge,

01:02:32toh socho socho and iska soch ke answer yaha mat dalna,

01:02:36iska soch ke answer video ke neeche comment karke zarur dalna,

01:02:40I'll be waiting and giving a heart to all the correct answers,

01:02:45yeh wala telegram group hai, bahot bachche bahot der se puchh rahe the mir se,

01:02:48Vedantu Math ka telegram group, yeh kaha hai yaar, yeh isi video ke neeche hai,

01:02:52kaha gaya shaitaan, pakdo ise, yeh raa, isi video ke neeche aap jaate ho,

01:02:58so yeh raa, join the telegram group now,

01:03:03toh aap sabse pehle telegram app ko download karte ho,

01:03:07play store se kar lena, then you click on this,

01:03:11agar aapka app downloaded hoga, tabhi yeh karikram aage ho sakta hai,

01:03:15varna nahi, and then you just have to click on join the group,

01:03:19abhi yeh ho nahi raa, kyunki system mein telegram nahi hai,

01:03:23toh yaha iska faida kya hota hai, of course,

01:03:26ek toh aapko notes milte hain, within 24 hours aapke saath free pdf share hoti hai,

01:03:31secondly, aapko pata chalta hai, kahi bachche bolte hain,

01:03:34ek toh bolungi, jab channel ko subscribe karte ho na,

01:03:37toh bell icon ko zarur hit kiya karo, zor se maara karo,

01:03:41usse aapko saari notifications aati hai,

01:03:44varna aapki class miss ho sakti hai,

01:03:46doosi cheez, class ka yaar poora schedule,

01:03:49aapke saath yaha bhi share hota hai every day,

01:03:52and mujhe agar aapse koi baat karne hai,

01:03:54then this is the official forum,

01:03:56theek hai, toh definitely aap yaha se jod sakte ho,

01:03:59bilkul free of cost hai,

01:04:00and aapka mobile number bhi share nahi hota,

01:04:04second thing, bachchu,

01:04:07vidantu ke learning app ko download karna mat bhoolna,

01:04:11yaar 5 million se zyada iske downloads ho chuke hain,

01:04:15and aap toh mai yeh bolti ho,

01:04:17agar mujh pe vishwas nahi toh google pe toh hai,

01:04:20google pe jao, check karo,

01:04:22google ne humko user's choice award diya hai,

01:04:25toh kuch na kuch toh hoga na,

01:04:27aapko definitely ja ke yeh check karna hai,

01:04:29yaha pe bohot saari live classes hoti hain,

01:04:32live quizzing bhi hoti hai aap toh,

01:04:34plus you get a lot of practice material,

01:04:37and yeh sab bilkul free hai,

01:04:38aisa kuch nahi hota,

01:04:39ki kuch din ke liye free hai,

01:04:41phir we will ask for subscription charges,

01:04:43no, it's absolutely absolutely free,

01:04:46toh pehla kaam yahi karo,

01:04:48yeh kaam toh karke jaana hi jaana hai,

01:04:51abhi bataya tha na kyu,

01:04:53chalo, I'll see you guys super duper soon,

01:04:55till then thank you so much for watching,

01:04:57bye bye.

01:05:02Thanks for watching.