MATH 221 Test 1 Name________________

Instructions: Answer all the questions on the paper provided. Show all your work so that partial credit may be given.

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

2. Find and classify the discontinuities of the function defined below. Show all the necessary limits and clearly specify the discontinuities. (20)

.

3. Let . Then (20)

a) Find the equation of the line tangent to the graph of y = f(x) at the point corresponding to x = -1.

b) Find all points on the graph of y = f(x) at which the tangent lines are parallel to the line y = 15x + 4 and find the equations of the tangent lines at those points.

4. Find each of the following limits: (15)

a) = ________

b) ________

c) ________

5. Solve the following inequality and express your solution in interval notation: (10)

.

6. Sketch the graph of a function y = f(x) that satisfies the following in the graphical space below. f has a jump discontinuity at x = 0 and a removable discontinuity at x = 2. .