Question

How do you find the limit of `(2+x)^(1/x)` as x approaches `0^-`?

Answer 1

The limit is `0`. For "how" please see below.

Explanation:

Informally

As `xrarr0-`, `(2+x)rarr2` and `1/x rarr-oo`.

So as `xrarr0^-` we have a quantity close to `2` being raised to a very big negative power.

`2` to a big negative is the same as
`1` over (`2` to a big positive power) which is
`1` over a big number and that is close to
`0`.