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Evaluate lim(xto0) (e^(sinx)-(1+sinx))/(...

Evaluate `lim_(xto0) (e^(sinx)-(1+sinx))/((tan(sinx))^(2))`

Text Solution

Verified by Experts

`underset(xto0)lim(e^(sinx)-(1+sinx))/((tan(sinx))^(2))`
`=underset(hto0)lim(e^(h)-(1+h))/((tan h)^(2))" "`(where `sin x=h`)
`=underset(hto0)lim((1+h+(h^(2))/(2!)+* * * )-(1+h))/((h+(h^(3))/(3)+* * * )^(2))`
`=underset(hto0)lim((h^(2))/(2!))/(h^(2))`
`=1/2`
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