Question

Lim x->0^+ (e^x+x)^(1/x)

please use L=(e^x+x)^(1/x) ln(L) so on if you are going to do it that way

Answer 1

lim (e^x - 1)/x = e^0 -1/0 =1-1/0 = (0/0)
x->0

l'hopitals rule (e^x-1)'/x' = e^x

lim e^x =1
x->0
\[\lim (e^x - 1)/x = e^0 -1/0 =1-1/0 = (0/0) x->0 l'hopitals rule (e^x-1)'/x' = e^x \lim e^x =1 x->0\]

Answer 2

How did you get the exponent down?