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Evaluatelim(xto0) (2^(x)-1)/(sqrt(1+x)-1...

Evaluate`lim_(xto0) (2^(x)-1)/(sqrt(1+x)-1).`

Text Solution

Verified by Experts

We have
`underset(xto0)lim(2^(x)-1)/(sqrt(1+x)-1)" "`(0/0 from)
`=underset(xto0)lim(2^(x)-1)/(sqrt(1+x)-1)((sqrt(1+x)+1))/((sqrt(1+x)+1))`
`=underset(xto0)lim(2^(x)-1)/(x)underset(xto0)lim(sqrt(1+x)+1)`
=(log2)2
=log4
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