MATH 221 – Review Exercises for Test 1

1. Let . Compute using the limit definition of the derivative.

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

.

3. . Let .

a) Find the equation of the line tangent to the graph of y = f(x) at the point corresponding to x = 2.

b) Find all points on the graph of y = f(x) at which the tangent lines are parallel to the line y = 6x + 4 and find the equations of the tangent lines at those points.

4. . Solve the following in interval notation: .

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

6. Find the equation of the line tangent to the graph of at (1,5).

7. Show that (0,3), (6,0), and (7,2) are the vertices of a right triangle.