using L'Hospital's rule, evalutate; LIM as x->0 e^x +cos x / e^x + sin x

Question

I'm at LIM x->0 e^x+cosx / e^x +sinx but now I at a lost as to how to proceed.

Answer 1

Who need's L'Hospital's Rule?
e^x + cosx --> 1 + 1 = 2
e^x + sinx --> 1 + 0 = 1

answer: 2/1 = 2

You only need L'Hospital's Rule when you wind up with 0/0 or ∞/∞

Unless the problem has a typo . . .