Final Review
1. Find the limit if it exists.
2. Find an equation of the tangent line to the curve
at the point (3, 135).
3. Evaluate the limit.
4. Evaluate the limit.
5. Evaluate the limit.
6. Find the vertical asymptotes of the function.
7. For
, determine whether f is continuous from the right, from the left, or neither.
8. Find the point at which the given function is discontinuous.
9. Find an equation of the tangent line to the parabola
10. Evaluate the limit.
11. Find the limit.
12. Evaluate the limit.
13. Determine the infinite limit.
14. Evaluate the limit.
15. For the function
whose graph is shown, state the following.
at the point (3, 27).
16. Find the points on the curve
where the tangent is horizontal.
17. Find the equation of the tangent to the curve at the given point.
18. Differentiate.
19. If a ball is thrown vertically upward with a velocity of 200 ft/s, then its height after t seconds is
.
What is the maximum height reached by the ball?
20. Find
by implicit differentiation.
21. Calculate
.
22. A spherical balloon is being inflated. Find the rate of increase of the surface area
radius r when r = 1 ft.
with respect to the
23. Differentiate the function.
24. Find an equation of the tangent line to the curve.
at
25. A plane flying horizontally at an altitude of 4 mi and a speed of 465 mi/h passes directly over a radar station.
Find the rate at which the distance from the plane to the station is increasing when it is 10 mi away from the
station. Round the result to the nearest integer.
26. Calculate
.
27. Find the first and the second derivatives of the function.
28. If
, find
29. If
and
30. If
find
.
, find
when
.
.
31. Differentiate.
32. The position function of a particle is given by
When does the particle reach a velocity of 52 m/s?
33. Differentiate.
34. Differentiate.
35. Find an equation of the tangent line to the curve
at the point
36. Find the derivative of the following function and calculate it for
.
to the nearest tenth.
37. Find all points at which the tangent line is horizontal on the graph of the function.
38. Calculate
.
39. Find
, if
.
40. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of
28 ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? Round the
result to the nearest hundredth if necessary.
41. Use the given graph of f to find the Riemann sum with six subintervals. Take the sample points to be left
endpoints.
42. The velocity function (in meters per second) is given for a particle moving along a line. Find the distance
traveled by the particle during the given time interval.
43. Find the area of the region that lies under the given curve.
Round the result to the nearest thousandth.
44. Evaluate.
Final Review
Answer Section
FREE RESPONSE
1. ANS:
PTS: 1
2. ANS:
PTS: 1
3. ANS:
263
PTS: 1
4. ANS:
0
PTS: 1
5. ANS:
1/8
PTS: 1
6. ANS:
PTS: 1
7. ANS:
neither
PTS: 1
8. ANS:
4
PTS: 1
9. ANS:
PTS: 1
10. ANS:
213
PTS: 1
11. ANS:
1/3
PTS: 1
12. ANS:
0
PTS: 1
13. ANS:

PTS: 1
14. ANS:
PTS: 1
15. ANS:

PTS: 1
16. ANS:
(1, 6), (2, 21)
PTS: 1
17. ANS:
PTS: 1
18. ANS:
PTS: 1
19. ANS:
1000
PTS: 1
20. ANS:
PTS: 1
21. ANS:
PTS: 1
22. ANS:
8
PTS: 1
23. ANS:
PTS: 1
24. ANS:
PTS: 1
25. ANS:
456
PTS: 1
26. ANS:
PTS: 1
27. ANS:
PTS: 1
28. ANS:
PTS: 1
29. ANS:
465
PTS: 1
30. ANS:
PTS: 1
31. ANS:
PTS: 1
32. ANS:
9
PTS: 1
33. ANS:
PTS: 1
34. ANS:
PTS: 1
35. ANS:
PTS: 1
36. ANS:
0.1
PTS: 1
37. ANS:
PTS: 1
38. ANS:
PTS: 1
39. ANS:
PTS: 1
40. ANS:
12.52
PTS: 1
41. ANS:
8
PTS: 1
42. ANS:
54
PTS: 1
43. ANS:
2.092
PTS: 1
44. ANS:
20/3
PTS: 1