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f:R->R is defined by f(x)={(cos3x-cosx)/...

`f:R->R` is defined by `f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0` and `f` is continuous at `x=0;` then `lambda=`

A

`-2`

B

`-4

C

`-6`

D

`-8`

Text Solution

Verified by Experts

The correct Answer is:
B
If f is continous x=0 then,
`underset(x to 0)lim f(x)=f(8)`
`Rightarrow underset(x to 0)lim (cos 3x-cosx)/(x^(2))=lambda`
`Rightarrow underset(x to 0)lim (-2sin 2x sinx)/(x^(2))=lambda`
`Rightarrow -4 underset(x to 0)lim ((sin 2x)/(2x))((sin x)/(2x))=lambdaRightarrow -4xx1xx1=-4`
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