Subsections

• Purpose
• Getting Started
• Exercises

Differentiation and Solving Systems of Equations

Purpose

The purpose of this lab is to introduce you to Maple commands for differentiation that we will need in subsequent labs and to introduce you to Maple techniques for solving systems of equations.

Getting Started

For this lab, we are trying something a little different. The background material, examples, and exercises are all in a Maple worksheet. To complete this lab, you copy that worksheet to your home directory with the following command, which must be run in a terminal window, not in Maple.

cp /math/calclab/MA1023/Solving2.mws ~

Once you have copied the worksheet over, you can load it into Maple and get started on the lab.

Exercises

1. First, enter the following functions in Maple. Then compute the derivatives using the diff command for the first function and the D operator for the second function.
   1. $$f(x) = \cos^3(x^2+4) - \exp(\sqrt{x^2+4})$$
   2. $$g(x) = \frac{x^3+7x-2}{x^3+6x^2-2x+8}$$
2. Find the equation of the circle that passes through the three points $(0.5,0.2)$, $(1.3,-4.2)$, and $(2,0.7)$. Use the implicitplot command to plot the circle. (Hint - the general equation for a circle is given below.)
   
   $$(x-a)^2 + (y-b)^2 = r^2$$
   
   

3. Solving implicitly, find where the circle from the previous exercise intersects the parabola $y=x^2+2x-5$.