MATH 221 Test 1 Fall 2002 Name_________________

Instructions: Answer all questions on the paper provided. Show all your work so that partial credit may be given. You may use a calculator on all parts of this test.

1. Let . Compute using the limit definition of the derivative. (15)

2. Show that the point (1,-4) is on the tangent line to the graph of at (2,4).

(10)

3. Solve the following inequality and express your solution in interval notation:

. (10)

4. Find and classify the discontinuities of the following function. Include all the limit computations necessary for your solution. (20)

5. a) Find the equation of the line tangent to at x = 1. (25)

b) Find the equation of the line perpendicular to the tangent line to at the point given by x = -2.

c) Find all points on the graph of at which the tangent lines are perpendicular to the line .

6. Sketch the graph of a function, f(x), such that f(1) = 0, f(-1) = 2, f has an essential discontinuity at x = -3, f has a removable discontinuity at x = -1, and f has a jump discontinuity at x = 1. (20)