Question #1956

Evaluate the limit. (If you need to use -infinity or infinity, enter -INFINITY or INFINITY.)

lim x->0 (e^x-e^-x-2x)/(x-sin(x))

lim x->0 (e^x-e^-x-2x)/(x-sin(x))

Expert's answer

lim _{x->0} (e^{x}-e^{-x}-2x)/(x-sin(x)) = lim _{x->0} (e^{x}+e^{-x}-2)/(1-cos(x)) = lim _{x->0} (e^{x}-e^{-x})/(-sin(x))=lim _{x->0} (e^{x}+e^{-x})/(-cos(x)) ->2/(-1) = -2

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