Answer to Question #1956 in Calculus for Vigi

Question

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))

Answer 1

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