Question

Limit of `lim_(x→0^+)(e^x+x)^x`?

Answer 1

`lim_(x->0^+)(e^x+x)^x=1`

Explanation:

When given a limit, the first thing we should always do is plug the limiting value into the limit to see what we get. So

`lim_(x->0^+)(e^x+x)^x=(e^0+0)^0=1^0=1`

In fact, the function is continuous and so `lim_(x->0^-)(e^x+x)^x=1`