INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

May 7, 2020

Problem on Calculus | ISI-B.stat | Objective Problem 696

Try this beautiful problem on Calculus, useful for ISI B.Stat Entrance.

Problem on Calculus | ISI B.Stat Entrance | Problem 696


If k is an integer such that lim \(\{{cos}^n(k\pi/4) – {cos}^n(k\pi/6)\} = 0\),
then

  • (a) k is divisible neither by 4 nor by 6
  • (b) k must be divisible by 12, but not necessarily by 24
  • (c) k must be divisible by 24
  • (d) either k is divisible by 24 or k is divisible neither by 4 not by 6

Key Concepts


Calculus

Limit

Trigonometry

Check the Answer


Answer: (d)

TOMATO, Problem 694

Challenges and Thrills in Pre College Mathematics

Try with Hints


There are four options ,at first we have to check each options.....

If k is divisible by 24 then cos(kπ/4) = cos(kπ/6) = 1
\(\Rightarrow\) The limit exists and equal to RHS i.e. 0
If k is not divisible by 4 or 6 then cos(kπ/4), cos(kπ/6) both <1

Can you now finish the problem ..........

Therefore ,

lim cosn(kπ/4), cosn(kπ/6) = 0. so we may say that
\(\Rightarrow \)The equation holds.

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
enter