Math 122 Calculus for Biology II Fall Semester, 2000 Lab Help	21-Sep-00
	San Diego State University

This page is designed to provide helpful information about the laboratory questions.

Question 1: This question allows you to experiment with trigonometric functions to build intuition. This problem examines properties like the period and oscillatory behavior of the trigonometric functions, sine and cosine. It should also reinforce a few of the Maple commands that you learned. (Don't forget the summary of the Maple commands on the special Maple help sheet.) Maple should help with the differentiation and finding values of extrema and intercepts.

Question 2: This problem gives you practice determining the period of a periodic function. The y-value of the maximum and minimum should be easy to obtain by simply using the fact that the cosine function has a maximum value of 1 and a minimum value of -1. The x-values at the extrema are most easily found using Maple's fsolve function, but many can also be found by interpreting the periodicity of the function. This is primarily a graphing exercise, which uses those capabilities of either Excel or Maple. Below shows you one means of entering the sum of two functions into Maple:

Enter the two functions, f(x) and g(x) as before

> f := t -> cos(3*t); g := t -> cos(5*t);

Combine the functions

> F := t -> f(t)+g(t); F(t);

Putting in the additional F(t) makes Maple print out the correct function for you. Notice that, because Maple is case sensitive, we can use f(t) and F(t) as different functions.