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

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

Discussion

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