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lim(x->0) (2^x-1)/(sqrt(1+x)-1)...

`lim_(x->0) (2^x-1)/(sqrt(1+x)-1)`

A

2

B

`log_(e )2`

C

`(log_(e )2)/(2)`

D

`2log_(e )2`

Text Solution

Verified by Experts

The correct Answer is:
D
`lim_(x to 0) (2^(x) -1)/(sqrt(1+x)-1) = lim_( x to 0) (2^(x)-1)/(x) xx (x)/(sqrt(1+x)-1) xx (sqrt(1+x) +1)/(sqrt(1+x) -1) =log 2 lim_(x to 0) (sqrt(1+x) +1) =2log 2`
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