Use your graphing calculator to evaluatelimit as x goes to infinity of the quantity 1 plus x all raised to the power of 4 divided by x. (2 points)

0

1

e⁴

2.

Use your calculator to select thebestanswer below: limit as x goes to infinity of the quotient of the cube of the quantity 2 times x minus 1^3 and negative 1 raised to the x power

(2 points)

2

2

does not exist

0

3.limit as x approaches a of the quotient of the quantity x minus a and the quantity the square root of x minus the square root of a equals

(2 points)

-2 square root a

2 square root a

square root a

2a

4.

FindFind the limit as x goes to 0 of the quotient of the quantity x plus 1 minus the square of cosine x and 3 times the sine of x. (2 points)

Does not exist

3

0

1/3

5.

Iflimit as x approaches zero of f of x equals three and limit as x approaches zero of g of x equals one , then find limit as x approaches zero of the quantity f of x plus g of x squared. (2 points)

40

-4

16

28

6.Evaluate limit as x approaches 0 of the quotient of the absolute value of the quantity x minus 1 and x minus 1

. (2 points)

does not exist

0

1

-1

7.

Evaluate limit as x goes to 3 of the quotient of the quantity 1 divided by x minus 1 third and the quantity x minus 3. (2 points)

-1/9

1/9

1/27

1/3

8.

Evaluatelimit as x goes to 0 of the quotient of the sine of 5 times x and 6x. (2 points)

1

5/6

1/6

Does not exist

9.

If f is a continuous function with odd symmetry andlimit as x approaches infinity of f of x equals 6, which of the following statementsmustbe true? (2 points)

I.limit as x approaches infinity of f of x equals 6

II. There are no vertical asymptotes.

III. The lines y = 6 and y = -6 are horizontal asymptotes

All statements are true.

I only

II only

III only

10.

What are the horizontal asymptotes of the function f of x equals the quotient of 5 times the square root of the quantity x squared plus 9 and x? (2 points)

y = 5 only

y = -5 only

y = -5 and y = 5

y = 0

11.

Which one or ones of the following statements is/are true? (2 points)

I. If the line y = 2 is a horizontal asymptote of y = f(x), then f is not defined at y = 2.

II. If f(5) > 0 and f(6) < 0, then there exists a number c between 5 and 6 such that f(c) = 0.

III. If f is continuous at 2 and f(2)=8 and f(4)=3, thenthe limit as x approaches 2 of f of the quantity 4 times x squared minus 8 equals 8.

All statements are true.

I only

II only

III only

12.

FindFind limit as x goes to infinity of the quotient of x cubed plus 9 times x squared plus 7 times x and negative 3 times x squared minus 4 times x plus 1(2 points)

1/3

0

-

13.

Evaluatelimit as x goes to 2 from the right of the quotient of x and the quantity the square root of the quantity x squared plus 4. (2 points)

1/square root 2

-1 square root 2

0

does not exist

14.

Which of the following are the equations of all horizontal and vertical asymptotes for the graph off of x equals x divided by the quantity x times the quantity x squared minus 16? (2 points)

y = 0, x = -4, x = 4

y = 1, x = -4, x = 4

y = 0, x = -4, x = 0, x = 4

y = 1, x = -4, x = 0, x = 4

15.

Evaluatelimit as x approaches 1 at f of x for f of x equals the quantity 5 times x minus 10 for x less than 1, equals 1 for x equals 1 and equals negative 3 times x minus 2 for x greater than 1. (2 points)

3

-5

1

does not exist

16.

Where isf of x equals the quotient of x plus 2 and x squared minus 2 times x minus 8discontinuous? (2 points)

x = -2

x = 4

x = -2 and x = 4

f(x) is continuous everywhere

17.

Which of the following are continuous for all real values of x? (2 points)

I.f of x equals the quotient of the quantity x squared plus 5 and the quantity x squared plus 1

II.g of x equals the quotient of 3 and x squared

III.h of x equals the absolute value x

I only

II only

I and II only

I and III only

18.

Which of the followingmustbe true for the graph of the functionf of x equals the quotient of the quantity x squared minus 16 and the quantity 4 times x minus 16? (2 points)

There is:

I. a vertical asymptote at x = 4

II. a removable discontinuity at x = 4

III. an infinite discontinuity at x = 4

III only

I only

I, II, and III

II only

19.

What is the average rate of change of y with respect to x over the interval [-1, 2] for the function y = 3x + 2? (2 points)

1

3

1/3

9

20.

What is the instantaneous slope of y =-7/xat x = 3? (2 points)

7/9

-7/3

7/3

-7/9

21.

The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 128 feet high is s(t) = -16t²- 32t + 128, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground? (2 points)

-96 ft/sec

256 ft/sec

0 ft/sec

112 ft/sec

22.

The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2rh+2r². Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6. (2 points)

24

34

64

20