MATH 222 Test 2 Part 1 Name_________________

Evaluate both integrals on this part. You may not use a calculator on this part. (20)

1.

2.

MATH 222 Test 2 Part 2 Name _______________

Answer all the questions on this part. You may use a calculator on all questions.

1. Compute the following limit and show explicitly where you use L”Hopital’s rule.

= (10)

2. Let a curve be defined by the parametric equations: . (20)

a) What are the x-y coordinates of the point given by t = 2?

b) Find all points on the curve where the tangent lines are horizontal.

c) Find all points on the curve where the tangent lines are vertical.

d) The curve encloses an area from t = -1 to t = 2. Find the area of this region.

3. Find the equation in standard form of the parabola with its focus at (-4,-4) and its directrix x = -8. (10)

4. . Using an appropriate substitution (write down the substitution) change the following integral to an integral of the product of trigonometric functions. Do not evaluate the integral further. (10)

5. Write the partial fraction expansion of the following rational function and determine the values of the constants. (15)

6. Plot the points given in polar coordinates in the graphical region below:

A (1,p/4), B (-2, 5p/6), C (3, 11p/4) (10)

7. Find the area enclosed by the curve . (5)