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If the function f(x)={((1-cosx)/(x^(2))...

If the function `f(x)={((1-cosx)/(x^(2))",","for "x ne 0),(k,"for " x =0):}` continuous at x = 0, then the value of k is

A

1

B

0

C

`(1)/(2)`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `lim_(x to 0) f(x)=f(0) rArr lim_(x to 0) (1-cosx)/(x^(2))=k`
`rArr lim_(x to 0)(-(-sinx))/(2x)=k" " `[using L'Hospital's rule]
`rArr (1)/(2)lim_(x to 0)(sinx)/(x)=k rArr k =(1)/(2)`
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