Chapter 4 - Exercises

1. Using Maple define the following functions and plot them simultaneously in a single graph

f1(x) = exp( - 0.3 x ² ) sin(x)

f2(x) = sin(x) cos(x)

Find the exact slope of these functions and plot these slope-functions.

2. Solve Question 1 using Excel. Use the Symmetric Difference method to compute the slope-functions.

3. Using Excel, define and plot the function

f(x) = sin(x) + cos(2x)

find its slope using the Symmetric Diffrence method and plot it in the interval [-p,p].

4. Solve Question 3 using Maple.

5. Analyze (i.e., find the zeros, minima, and maxima of) the function

f(x) = ( x + 2 ) / ( 3 + ( 3 * x ² + 1 ) ³ )

6. Analyze (i.e., find the zeros, minima, and maxima of) the function ( in the domain [-5,5] )

f(x) = x*x*x - 4 * cos(x)

6. Difficult problem (Maple)

The x & y velocity components are the derivatives (slope) of the x & y position functions. Calculate these for the Space Shuttle spiral motion toward the earth (see Section 4.4). Plot these x & y velocity functions as functions of time. Find the magnitude of the velocity vector as a function of time and plot it.

Any questions or suggestions should be directed to Michel Vallières at vallieres@physics.drexel.edu