Control-drag $f\left(x\right)\=\dots$
Context Panel: Assign Function

(Click here to see a detailed explanation of how to enter a piecewise-defined function in Maple.)

Figure 1.1.5(a), while not essential, is extremely revealing about the behavior of $f\left(x\right)$ near $x\=1$. The jump in the function shows that the two one-sided limits will not be equal, and that the limit itself will not exist.

Code for drawing Figure 1.1.5(a) is hidden behind the cell containing it. It can also be drawn interactively via the Plot Builder. (The relevant options are: in Basic Options set the range for x, in 2-D Options select the discont option, and in Global Options set the view for axis[2].)

The left-hand rule in $f$ can be obtained by simplifying $f$ under the assumption that $x<1$.

Context Panel: Evaluate at a Point≻$x\&equals;1$ 

The right-hand rule in $f$ can be obtained by simplifying $f$ under the assumption that $x\ge 1$.

Context Panel: Evaluate at a Point≻$x\&equals;1$ 

The limit from the left is the value of the left-hand rule taken at $x\&equals;1$.

The limit from the right is the value of the right-hand rule taken at $x\&equals;1$.

Expression palette: Limit template
Obtain the limit from the left.

Expression palette: Limit template
Obtain the limit from the right.

Expression palette: Limit template
Obtain the limit of $f$.