Figure 3.9.8(a) contains graphs of $\csc \left(x\right)$ (in black) and $\cot \left(x\right)$ (in red). The line $x\=0$ is a vertical asymptote for both curves, suggesting that as $x\to 0$, the difference $\csc \left(x\right)-\cot \left(x\right)$ tends to the indeterminate form $\infty -\infty$.

Figure 3.9.8(a) also suggests that the values of the functions near $x\=0$ are so similar that perhaps the limit of the difference $\csc \left(x\right)-\cot \left(x\right)$ might indeed be zero. Of course, this can be verified immediately in Maple via the calculation

The Context Panel provides access to the options All Solutions, Next Step, and Limit Rules, as per the figure to the right.

While the Context Panel lists both a "difference" and a "sum" rule, Maple treats a difference as if it were a sum, thereby making no essential distinction between the two rules. Thus, where Table 1.3.1 distinguishes between a Sum and a Difference rule, Maple considers both to be the single Sum rule.

In addition, the Student Calculus1 package contains a ShowSolution command that can be applied to the inert form of the limit operator. The limit operator can be converted to the inert form through the Context Panel by selecting the options 2-D Math≻Convert To≻Inert Form.

Tools≻Load Package: Student Calculus 1

Control-drag $\underset{x\to 0}{lim}\dots$

Context Panel: Student Calculus1≻All Solution Steps