MATH 222 Test 1 Name_____________________

Instructions: Answer all the questions on the paper provided and clearly indicate your answers. Show your work. You may use the calculator on all questions. Give the sequence of keystrokes if you are evaluating an integral with the calculator.

I. Evaluate each of the following limits: (24)

1. 1.____________

2. 2.____________

3. 3.____________

4. 4.____________

II. Find the derivative of each of the following: (12)

1. 1.____________

2. 2.____________

III. Completely evaluate the following integrals: (24)

1.

2.

IV. Make the appropriate substitutions that transform the following integral to the integral of a product of trig functions. Do not evaluate the resulting integral. (10)

V. Simplify the following: (5)

VI. Solve the following for x: (5)

VII. Two species, A and B, of worms are being grown in a laboratory. At the beginning of the experiment, t = 0, there were 100 worms of species A. After 8 days there were 200 of species A. At the same time (t = 8) there were 200 of species B. 4 days after the beginning there were 100 of species B. Assume that both species are undergoing exponential growth. (20)

1. Find an expression for the number of individuals of species A in terms of t (t in days).

2. What was the population of species B at time t = 0?

3. What is the population of species A when species B reaches 1000 individuals?