How do I find one-sided limits graphically?

1 Answer
Apr 21, 2017


Observe the y value that the graph approaches.


In order to find a one-sided limit graphically, you much observe the graph to find the point at which the graph is approaching. As opposed to standard limits, one-sided limits are only dependent on one side of a given x value. Locate this x value on the graph and see where the graph is approaching from the side you want.

For example, look at the following graph f(x). graph{sqrt(x-5)+10 [-28.86, 28.88, -14.44, 14.42]}
On the graph, the right sided limit of f(5) is 10 because that is the y value being approached on the left side, but there is no left sided limit because there is no graph on that side.

On piecewise functions, this may not be the cases. It is not necessary for the left and right side limits to be the same number, or for f(c) to be defined.