ST 552

Calculus on a Computer

Assignment 2 Inverse Functions, logarithms & exponentials

1. Use MAPLE to plot the following. Which have inverses? Why? Find them if you can.

a.

b.

c.

d.

2. Plot all six basic trig functions. What are their periods?

3. Plot 2sin(3x)-cos(3x). What is the period? The amplitude?

4. Evaluate the following:

a. sin(arcos(.3))

b. cos(arctan(10))

c. tan(arcsin(-.2))

5. What is sin(arcsin(x))? How about arcsin(sin(x))? Explain.

6. Let A = the angle in the second quadrant with sin(A) = .7, and find all five other trig functions of A.

7. Graph . What do you notice? Prove it.

8. Assume that . What does this say about Now take the log base a of both sides of . Derive the change of base formula.

9. How much interest does $1000 earn in a year if it is compounded:

a. Monthly?

b. Daily?

c. Hourly

d. Continuously?

10. If T(t) is the temperature of an object, and is the room temperature, then T(t) is given by a formula of the form (T(0)is the temperature at time 0, and k is a constant.) Suppose my cup of coffee starts out at 180°F, and after 5 minutes it is 140°F. Assuming room temperature is 70°F,

a. Find k.

b. Find the temperature after 15 minutes.

c. When will the temperature be 100°F?