Practice Exam 3
Review Packet
Chapters 10 and 11
1. Estimate the limit numerically. (If the limit does not exist, enter NONE.)
2. Estimate the limit numerically. (If the limit does not exist, enter NONE.)
3. Estimate the limit numerically. (If the limit does not exist, enter NONE.)
4. Estimate the limit numerically. (If the limit does not exist, enter NONE.)
5. The graph of f is given. Use the graph to compute the quantities asked for, if a = 22.
(a)
(b)
(c)
(d)
6. The graph of f is given. Use the graph to compute the quantities asked for, if a = 20. (If
the quantity does not exist, enter NONE. Enter +INFINITY for + and -INFINITY for as needed.)
(a)
(b)
(c)
(d)
(e)
(f)
7. The graph of a function f is given.
Determine whether f is continuous on its domain.
Find the point of discontinuity. (If there is no such point, enter NONE.)
8. The graph of a function f is given.
Determine whether f is continuous on its domain.
Find the point of discontinuity.
9. Use a graph of f or some other method to determine what, if any, value to assign to f(a) to
make f continuous at x = a. (If there is no such value, enter NONE.)
10. Calculate the limit algebraically. (If the limit does not exist, enter NONE. Enter
+INFINITY for + and -INFINITY for - as needed.)
11. Calculate the limit algebraically. (If the limit does not exist, enter NONE. Enter
+INFINITY for + and -INFINITY for - as needed.)
12. Calculate the limit algebraically. (If the limit does not exist, enter NONE. Enter
+INFINITY for + and -INFINITY for - as needed.)
13. Calculate the limit algebraically. (If the limit does not exist, enter NONE. Enter
+INFINITY for + and -INFINITY for - as needed.)
14. Calculate the limit algebraically. (If the limit does not exist, enter NONE. Enter
+INFINITY for + and -INFINITY for - as needed.)
15. Calculate the limit algebraically. (If the limit does not exist, enter NONE. Enter
+INFINITY for + and -INFINITY for - as needed.)
16. Calculate the average rate of change of the given function over the interval [0, 2].
x 0 1 2 3
f(x) -5 7 3 2
17. Calculate the average rate of change of the given function over the interval [-3, -1].
x -3 -2 -1 0
f(x) -2.5 0 -1.5 0
18. Calculate the average rate of change of the given function over the given interval.
19. Calculate the average rate of change of the given function over the given interval.
20. Calculate the average rate of change of the given function f over the intervals [a, a + h]
for the following h. (Technology is recommended for the cases h = 0.01, 0.001, and
0.0001.)
h=1
h = 0.1
h = 0.01
h = 0.001
h = 0.0001
21. Estimate the derivative from the table of average rates of change. (Give the answer to one
decimal place.)
1 0.1 0.01 0.001
0.0001
h
Ave. rate of change of r over [3, 3 + h] 2.1 2.44 2.488 2.49948 2.4999983
h
-1 -0.1 -0.01 -0.001
-0.0001
Ave. rate of change of r over [3 + h, 3] 3.7 2.60 2.513 2.50086 2.5000040
r'(3) =
22. Estimate the indicated derivative by any method.
23. Compute f '(a) algebraically for the given value of a. (limit of the difference quotient)
24. Compute f '(a) algebraically for the given value of a. (limit of the difference quotient)
25. Compute f '(a) algebraically for the given value of a. (limit of the difference quotient)
26. Compute f '(a) algebraically for the given value of a. (limit of the difference quotient)
27. Find the equation of the tangent to the graph at the indicated point. (Enter the equation in
the y = mx + b form.)
28. Find the equation of the tangent to the graph at the indicated point. (Enter the equation in
the y = mx + b form.)
29. Use the shortcut rules to mentally calculate the derivative of the given function.
30. Use the shortcut rules to mentally calculate the derivative of the given function.
31. Obtain the derivative dy/dx.
32. Find the derivative of the function.
33. Find the derivative of the function.
34. Find the derivative of the function.
35. Find the derivative of the function. (First expand the given function.)
36. For the given cost function, find the marginal cost at the given production level x.
37. Find the marginal cost, marginal revenue and marginal profit functions.
38. Your monthly profit (in dollars) from selling magazines is given by the following
function, where x is the number of magazines you sell in a month. If you are currently
selling x = 50 magazines per month, find your profit and your marginal profit. Interpret
your answers. (Give your answers to the nearest cent.)
39. The cost C of building a house is related to the number k of carpenters used and the
number x of electricians used by the formula.
(a) Assuming that 10 carpenters are currently being used, find the cost function, the marginal
cost function and average cost function, all as functions of x.
Cost function
Marginal cost function
Average cost function
(b) Use the functions you obtained in part (a) to compute marginal cost and average cost when x
= 15. (Give your answers to the nearest cent.)
40. Do the following for the given function.
(a) Calculate the derivative without using the quotient rule.
(b) Use the quotient rule to find the derivative. Check that you obtain the same answer.
Calculate dy/dx. Simplify your answer.
41. Calculate dy/dx. Simplify your answer.
42. Calculate dy/dx. You need not expand your answer.
43. Calculate dy/dx. You need not expand your answer.
44. Calculate dy/dx. You need not expand your answer.
Calculate dy/dx. You need not expand your answer.
Calculate dy/dx. You need not expand your answer.
Calculate dy/dx. You need not expand your answer.
Find the equation of the line tangent to the graph of the given function at the point with the
indicated x-coordinate.
Calculate the derivative of the function.
Calculate the derivative of the function.
Calculate the derivative of the function.
Calculate the derivative of the function.
Calculate the derivative of the function.
Calculate the derivative of the function.
Calculate the derivative of the function.
Calculate the derivative of the function.
Calculate the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.
Find the derivative of the function.