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Let f(x)= {(((xsinx+2cos2x)/(2))^((1)/(x...

Let `f(x)= {(((xsinx+2cos2x)/(2))^((1)/(x^(2))),,,,xne0),(e^(-K//2),,,,x=0):}` if `f(x)` is continous at `x=0` then the value of k is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`becauseunderset(xto0)limf(x)=e^(underset(xtoo)(lim)((xsinx+2cos2x)/(2)-1)(1)/(x^(2))=e^(-3//2))`
and `f(0)=e^(-k//2)`
`thereforek=3`
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