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The value of f(0) so that f(x)=((-e^(x)...

The value of f(0) so that `f(x)=((-e^(x)+2^(x)))/(x)` may be continuous at x = 0 is

A

`log((1)/(2))`

B

0

C

4

D

`-1+log 2`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, f(x) is continuous at x = 0.
`therefore lim_(x to 0) f(x)=f(0)`
`rArr lim_(x to 0) (-e^(x)+2^(x))/(x)=f(0)`
`rArr lim_(x to 0) (-e^(x)+2^(x)log2)/(1)=f(0) " " `[by L' hospital's rule]
`therefore f(0)=-1+log 2`
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