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

1 Answer
May 19, 2017

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]}