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Evaluate lim(x to 0) (2^(x)-1)/((1+x)^...

Evaluate `lim_(x to 0) (2^(x)-1)/((1+x)^(1//2)-1)`

A

`(1)/(8sqrt(3))`

B

`(1)/(4sqrt(3))`

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
`log4`
`underset(xto0)lim(2^(x)-1)/((1+x)^(1//2)-1)`
`=underset(xto0)lim(2^(x)log2)/((1)/(2)(1+x)^(-1//2))" "`(Applying L'Hospital's rule)
`=2log2`
`=log4`
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