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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.

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