Let f(x) = (x(2^(x)-1))/( 1- cos x) fo...

Let ` f(x) = (x(2^(x)-1))/( 1- cos x)` for ` x ne 0` what choice of f(0) , if any, will make f (x) continuous at x = 0 ?

A

log2

B

`(1)/(2) log 2`

C

`(1)/(2log 2)`

D

2log2

Verified by Experts

The correct Answer is:

D

`lim_(x to 0) f(x) = lim_(x to 0) (x(2^(x)-1))/(1-cosx)`
`=lim_(x to 0) (2^(x)-1)/(x) *(x^(2))/(1-cos x)`
`=(log2)*((1)/((1)/(2)))=2log2`

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