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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+log2`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, f(x) is continuous at x=0
`thereforeunderset(xto0)(lim)f(x)=f(0)`
`impliesunderset(xto0)(lim)(-e^(x)+2^(x))/(x)=f(0)`
`impliesunderset(xto0)(lim)(-e^(x)+2^(x)log2)/(1)=f(0)`
[by L'Hospital'r rule]
`impliesf(0)=-1+log2`.
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