Try this beautiful problem on Calculus, useful for ISI B.Stat Entrance.
If k is an integer such that lim \(\{{cos}^n(k\pi/4) – {cos}^n(k\pi/6)\} = 0\),
then
Calculus
Limit
Trigonometry
Answer: (d)
TOMATO, Problem 694
Challenges and Thrills in Pre College Mathematics
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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