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

May 19, 2017

${\lim}_{x \rightarrow {0}^{-}} = - \infty$

#### 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:

$1 + \frac{1}{- 0.1} = - 9$

$1 + \frac{1}{- 0.01} = - 99$

$1 + \frac{1}{- 0.001} = - 999$

The limit will intuitively keep growing negatively, so the limit as $x$ approaches $0$ will be $- \infty$.

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]}