MATH 222 Test 1 Name_______________

Instructions: Answer all the questions on the paper provided. You may use your calculator on all questions.

1. a) Write the partial fraction expansion of (16)

b) Determine the constants in the expansion in part a).

c) Evaluate

2. To evaluate requires the method of Integration by Parts. Compute the integral using integration by parts, explicitly showing the steps of the process. (15)

3. Evaluate the following limits. In each case state explicitly when you are using L’Hopital’s Rule. (12)

a)

b)

4. Using appropriate substitutions turn into an integral of the product of trigonometric functions. Do not compute the integral. (14)

5. Arlo has 10 pounds each of two radioactive elements – Giulianium and Clintonium. Giulianium has a half life of 12 minutes. The ten pounds of Clintonium decayed to 7 pounds in 10 minutes. (21)

a) Find the function M_G(t) for the mass of Giulianium at time t (in minutes).

b) Find the half-life of Clintonium.

c) How much of each element is left after 1 hour?

6) Evaluate showing all necessary limits. (15)

7) Show that is incorrect. (7)