MATH 221 Test 1 Fall 2003 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. Show all the steps of the computation of the limit. (15)

2. Solve the following inequality and express your solution in interval notation. (15)

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

4. Is the point (1,2) on the line tangent to the graph of at the point(-1,0)?

Briefly justify your answer. (10)

5. a) Find the equation of the line tangent to at x = 5. (20)

b) Find all points on the graph of at which the tangent lines are perpendicular to the line found in part a).

6. Sketch the graph of a function, f(x), such that f(1) = 2, f(-1) = 0, 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)