Question

How do you find `lim 1+1/x` as `x->0^-`?

Answer 1

`lim_(xrarr0^-) = -oo`

Explanation:

You're trying to find the limit of the equation as `x` approaches `0` from the left.

One way to do this is to substitute values in for `x` that are successively closer and closer to `0` (negative values, since it's from the left), until the limit becomes understood:

`1+1/(-0.1) = -9`

`1+ 1/(-0.01) = -99`

`1 + 1/(-0.001) = -999`

The limit will intuitively keep growing negatively, so the limit as `x` approaches `0` will be `-oo`.

Ultimately, if you have the option to, graphing the equation is a surefire way to check this limit:
graph{1+1/x [-5, 5, -7.8, 7.8]}