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]}