Get inspired by the success stories of our students in IIT JAM 2021. Learn More 

June 4, 2020

ISI MStat 2018 PSA Problem 8 | Limit of a Function

This is a beautiful problem from ISI MStat 2018 PSA Problem 8 based on limit of a function. Try yourself and use hints if required.

Limit of a Function - ISI MStat Year 2018 PSA Question 8


The value of \( \lim _{x \rightarrow \infty}(\log x)^{1 / x} \)

  • (A) is e
  • (B) is 0
  • (C) is 1
  • (D) does not exist

Key Concepts


Limit

L'hospital Rule

Check the Answer


Answer: is (C)

ISI MStat 2018 PSA Problem 8

Introduction to Real Analysis by Bertle Sherbert

Try with Hints


What is the form of the limit? Can you convert it to some known limit?

\(\infty^0\)
\(\frac{\infty}{\infty}\)
L'Hospital Rule

Let , \( \lim _{x \rightarrow \infty}(\log x)^{1 / x} \) =l (say) then taking log on both sides we get , \( \lim _{x \rightarrow \infty} \frac{ log( logx) }{x} \) =log (l) . Now we will apply L'hospital rule .

Applying L'hospital rule we get , log (l)= \( \lim _{x \rightarrow \infty} \frac{1}{logx x} \)= 0 \( \Rightarrow l=e^0 \Rightarrow l=1 \)

Hence , option (C) is correct .

ISI MStat 2018 PSA Problem 8
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com