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If f(x)={((1-cos x)/(x)",",x ne 0),(k","...

If `f(x)={((1-cos x)/(x)",",x ne 0),(k",",x=0):}` is continuous at x = 0, then the value of k is

A

0

B

`(1)/(2)`

C

`(1)/(4)`

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(x to 0)f(x)=lim_(x to 0) (1-cos x)/(x)=lim_(x to 0) (2 "sin"^(2)(x)/(2))/(4((x)/(2))^(2))*x =0`
Also, `f(0) =k`
Since, f(x) is continuous
`therefore lim_(x to 0) f(x)=f(0) rArr k =0`
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