Subsections

• MAPLE USAGE
• EXERCISES

TOPICS IN CALCULUS II

This lab presents exercises taken from several topics that are studied in MA 1022. Because this lab deals with multiple topics, you do not need to include a summary section in the lab report.

MAPLE USAGE

When solving an equation, it is possible to give names to the solutions so that they can be used without having to retype them. Essentially, you only need to give a name to the set of solutions. Try these commands to see how this works.

  > g:=6*x^4-35*x^3+22*x^2+17*x-5;

  > sol:=fsolve(g=0);

  > sol[1];

  > sol[2]+sol[4];

EXERCISES

1.

Find the total area bounded by the curve given by

and the x-axis. What do you need to check as you start this problem?

2.

Compute the total area bounded by the graph of the f of Exercise 1 and the graph of

3.

Consider $k(x) = \sqrt{x\sin(x)}$ on the interval $[0, \pi/2]$. Use Maple to find the c whose existence is guaranteed by the Mean Value Theorem for Integrals. Make sure that your answer is reasonable.

4.

Consider the function h defined below. Find the absolute minimum of h. Use Maple to find $h^\prime$, but explain how you could have found $h^\prime$ without Maple. Use Maple to plot h on the interval [-1,2].