11. Find the vertical asymptotes of the function.

17.  

Find the point at which the given function is discontinuous.

 

18. 

State the domain.

20. If for , find

3. The displacement (in feet) of a certain particle moving in a straight line is given by where t is measured in seconds. Find the average velocity over the interval [1, 1.8].

Select the correct answer. a. 0.865 b. 0.654 c. 0.765 d. 0.756 e. 0.745 f. 0.755

5. Find the limit, if it exists.

Select the correct answer.

a. b. c. d. e. limit does not exist6.  Find the limit.

Select the correct answer.

a. -1/2 b. c. d. e. limit does not exist 14. Determine where is discontinuous.

Select the correct answer.

a. b. c. d. e. 1.  The position of a car is given by the values in the following table. Find the average velocity for the

time period beginning when t = 2 and lasting 2 seconds.

t (seconds) 0 1 2 3 4 5s (feet) 0 18 35 74 110 175

Select the correct answer.

a.  35.5 b.  47.5 c.  39 d.  37.5 e.  33.5 1. If , find the following numbers.

 

3. Find the equation of the tangent to the curve at the given point.

1. The position function of a particle is given by 0,25.1 23 tttts .

When does the particle reach a velocity of 166 m/s?

Select the correct answer.

a. t = 7 secb. t = 8 sec c. t = 5 sec d. t = 3 sec e. t = 12 sec

2. If ,sincos4)( 2 xxxf find f '(x) and f ''(x).

Select all correct answers.

a.   )2cos(2)cos(4)( xxxf

b.   )cos(4)2cos(2)( xxxf

c.   )sin()2sin(4)( xxxf

d.   )2sin()sin(4)( xxxf

e.   )cos(2)2cos(4)( xxxf 4.  The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the

acceleration after 4.5 seconds.

ts 2sin

Select the correct answer.

a. 9 m/ 2s b. 9 m/ 2s

c.   0 m/ 2s d.   281 m/ 2s e. 281 m/ 2s

8. Use the linear approximation of the function at a = 0 to approximate the number .

Select the correct answer.

a.  3.02 b.  0.15 c.  7.44 d.  7.4 e.  2.25

7.  The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 24xS . Find the linear density when x is 1 m.

Select the correct answer. a. 4 b. 16 c. 8 d. 12 e. 18

2.  Evaluate.

4. Find the tangent line to the ellipse at the point .

Select the correct answer.

a.   b.   c.   d.   e.   none of these

8.  If a ball is thrown vertically upward with a velocity of 72 ft/s, then its height after t seconds is . What is the maximum height reached by the ball?

Select the correct answer. a. 6 ft b. 216 ft c. 36 ft d. 225 ft e. 81 ft

1. Find all the critical numbers of the function.

Select the correct answer.

a. b. c. d. e.  none of these

7.  How many points of inflection are on the graph of the function?

Select the correct answer.

a.  1 b.  2 c.  4 d.  3 e.  5

12. 

Sketch the curve.

,

Select the correct answer.

a.   

b.   

c.   

13. 

Find the inflection points for the function given.

,

Select the correct answer.

a.

b.

c.

d.

e. 17. 

Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L = 9 cm if one side of the rectangle lies on the base of the triangle. Round the result to the nearest tenth.

Select the correct answer.

a.  

9.5 cm , 3.9 cm

b.  

7.5 cm , 2.9 cm

c.  

4.5 cm , 4 cm

d.  

4.5 cm , 3.9 cm

e.  

4 cm , 3.91 cm

f.  

5.5 cm , 4.4 cm

18. A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of 6 mi/h and row a boat at 2 mi/h. How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth.

Select the correct answer.

a.  0.55 radians b.  She should walk around the lake from point A to point C. c.  She should row from point A to point C radians d.  0.34 radians e.  0.98 radians

2. Find the absolute maximum value of on the interval [- 6, 6].

Select the correct answer.

a.  5b.  6c.  7d.  0e.  1

15. 

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round the result to the nearest hundredth.

Select the correct answer.

a. 5.35 m b. 4.4 m c. 4.35 m d. 0 m e. 3.25 m

16. 

Let and be polynomials.

Find if the degree of is 5 and the degree of is 9.

Select the correct answer.

a. -4b. 9c. 4d. 0e. 5

6.  Find the area of the region that lies beneath the given curve.

Select the correct answer.

a. 1.500 b. - 1.500 c. 0.500 d. - 0.500 e. 1.4509. An animal population is increasing at a rate of per year (where t is measured in years). By

how much does the animal population increase between the fourth and tenth years? Select the correct answer.

a. 2,220 b. 4,362 c. 2,155 d. 2,064 e. 2,10014. 

Evaluate the integral.

Select the correct answer. The choices are rounded to the nearest hundredth. a. 109.00 b. 123.67 c. 102.33 d. 209.00 e. 23.67

15. 

Find the derivative of the function.

2

4

215)(x

dttxg

Select the correct answer.

a. b. c. d. 410 1x x e.

6.  If is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years 2 and 10?

Select the correct answer.

a. b.

4. 

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by and about the y-axis.

Select the correct answer.

a. b. c. d. e.

6.

Find the volume of the solid obtained by rotating the region bounded by and about the x-axis.

Select the correct answer.

a. b. c. d. e.

20. 

The temperature of a metal rod, 4 m long, is 3x (in degrees Celsius) at a distance x meters from one end of the rod. What is the average temperature of the rod?

Select the correct answer.

a. b. c. d. e.

13.

Find the average value of the function on the interval [1, 36].

Select the correct answer.

a. b. c. d. e.

4.  Evaluate the integral.

Select the correct answer.

a. 0 b. c. d. e.

13. A manufacturer of light bulbs wants to produce bulbs that last about 600 hours but, of course, some bulbs burn out faster than others. Let )(tF be the fraction of the company's bulbs that burn out before t hours. )(tF lies between 0 and 1.

Let )()( tFtr . What is the value of

0

?)( dttr

Select the correct answer.

a.

0

600)( dttr b.

0

1)( dttr c.

0

0)( dttr

d.

0

2)( dttr e. divergent

14. 

Evaluate the integral or show that it is divergent.

Select the correct answer.

a. 

b. 0 c. 

d. 

e. divergent

1.  Find the length of the curve.

Select the correct answer.

a. 

b. 

c.  d. 

e. 

2.  Find the length of the curve.

Select the correct answer.

a. 

b. 

c. 

d. 

e. none of these

3.  Find the length of the curve for the interval .

Select the correct answer.

a. 

b. 

c. 

d. 

e. 

2. is the solution of the differential equation . Find the solution that satisfies the

initial condition .

11.

Use the Chain Rule to find .

Select the correct answer.

a.

b.

c.

d.

e.

15. 

Find the equation of the normal line to the given surface at the specified point.

Select the correct answer.

a.  

b.  

c.

d.   e.  

10. 

Find the critical points of the function.

Select the correct answer.

a.  (-4, 4), (-6, 6), (10, -10) b.  (-6,6), (-8,8), (8, -8) c.  (-4,6), (-6,-10), (10, 4) d.  (4, 4), (6, 6), (-10, 0) e.  (-4,6), (-8,6), (8, -6)

12. 

At what point is the following function a local maximum?

Select the correct answer.

a. (1, -1) b. (-1, 1) c. (3, 1) d. (0, 1) e. (1, 1)13. 

At what point is the following function a local minimum?

Select the correct answer.

a. (-1, 2) b. (1, 6) c. (0, 0) d. (-1, 6) e. (-1, -6)14. 

Find all the saddle points of the function.

Select the correct answer.

a. b. c. d. e.

18. Find the area of the part of the plane that lies in the first octant.

6. Find the volume under and above the region bounded by and .

Select the correct answer.

a. b. c. d. e.

8.

Use polar coordinates to find the volume of the solid under the paraboloid and above the

disk .

Select the correct answer.

a. b. c. d. e.