Question

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

Answer 1

\[\lim_{x \rightarrow 0} (e ^{x}-e ^{-x}-2x)/x-\sin(x)\]

Answer 2

l'Hopital's Rule. apply it 3 times:

= limx->0 (e^x + e^-x - 2)/(1 - cosx)

= limx->0 (e^x - e^-x)/sinx

= limx->0 (e^x + e^-x)/cosx

= (1 + 1)/1 = 2

Answer 3

thanks a lot : )

Answer 4

nice solution

Answer 5

Smart, James!