# What is the purpose of a limit in calculus?

##### 1 Answer

Sep 6, 2014

A limit allows us to examine the tendency of a function around a given point even when the function is not defined at the point. Let us look at the function below.

Since its denominator is zero when

This tool is very useful in calculus when the slope of a tangent line is approximated by the slopes of secant lines with nearing intersection points, which motivates the definition of the derivative.