JEE Delight | ISI UGA 2024 | Q23 | 'Master Limits with Sandwich Theorem and Definite Integrals

In this video, we tackle a fascinating limit problem that perfectly illustrates the power of the Sandwich Theorem and Definite Integrals. This problem is crucial for students preparing for competitive exams like JEE Mains, JEE Advanced, ISI, and CMI.

🔍 Problem Breakdown:
We'll solve the limit:
lim n tends to infinity rlogr/n^2logn
Step-by-step, we'll guide you through the solution using the Sandwich Theorem and integrate the concepts of definite integrals for a clear understanding.

📚 What You'll Learn:

Application of Sandwich Theorem in limits
Understanding and solving definite integrals in limits
Tips and tricks for competitive exams like JEE Mains, Advanced, ISI, and CMI
👩‍🏫 Perfect For:

JEE Mains & Advanced aspirants
ISI and CMI candidates
Anyone looking to strengthen their calculus concepts
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#mathsmerizing #limits #SandwichTheorem #definiteintegrals #jeemains #jeeadvanced #ISI #cmi #competitiveexams #mathtricks #calculus

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[harshuldesai]

You can form r/n inside the log by adding (r/n)log(n). Split the limit into two: lim_{n->infty} -1/(4log(n)) + lim_{n->infty} (n+2)(n-1)/2n^2 = 0 + 1/2 = 1/2.

[subhrayanbarman]

Another way to solve this:
Let, An= 2log2+3log3+...+nlogn
and, Bn= n²logn
Then, ∆A=An-An-1=nlogn
~(2n-1)logn
∆A/∆B =1/2

[shivanshnigam]

Sir I turned the numerator in to a definite integral but with some ln(n) terms remaining so just wrote the definite integral as some constant then used LHopital and got 1/2 as the ans

[edu_in_iitg]

Handwriting dekhar ulti aa gayi re bhaiya 😅 anyways gr8 soln

[piyushraj]

stolz cesaro is also a good approach sir

[Your_Study_Buddy_SD]

This question seemed to be easy at first look but after a couple of calculations, realization strikes that oh boy this will take a twist.

This is a wonderful question.🤌👌