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Evalaute lim(xto0) (x2^(x)-x)/(1-cosx)...

Evalaute `lim_(xto0) (x2^(x)-x)/(1-cosx)`

Text Solution

Verified by Experts

The correct Answer is:
`log4`
`underset(xto0)lim(x(2^(x)-1))/(1-cosx)=underset(xto0)lim(2^(x)-1)/(x)xx(x^(2))/(1-cosx)`
`=log2underset(xto0)lim(x^(2))/(2"sin"^(2)(x)/(2))`
`=2log2=log4`
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