Exploring Calculus with Maple Introductory Calculus

We can use the limit() command to evaluate the limit of a function as \(x\) approaches \(a\text{.}\) The limit() command needs two parameters. The first parameter is the expression and the second parameter gives the value for a variable to approach.

The order of the parameters in the limit() command is important. An error message will be displayed if you switch the order of the parameters in the command and then try to execute it.

> f(x) := x^2 + 2*x -4;

> limit(f(x), x=3);

In this next example, it is important to note that \(h=0\) here means that \(h\) approaches \(0\text{,}\) but we are not simply substituting \(h=0\) into the expression. In fact, this expression is undefined at \(h=0\text{.}\)

> limit((f(x+h) - f(x))/h, h=0);