# CALCULUS

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

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1) Given that f(x) = , find f . Express the answer as a simplified fraction. 1) _______

A) – B) C) – D) Use the graph to evaluate the indicated limit and function value or state that it does not exist.

2) Find f(x) and f(0). 2) _______

A) Does not exist; 6 B) 6; 0 C) 0; does not exist D) 0; 6

Find the limit, if it exists.

3) Find:  3) _______

A) -11 B) C) 1 D) – 4) Given f(x) = -2 and g(x) = 5, find  . 4) _______

A) – B) – C) D) Sketch a possible graph of a function that satisfies the given conditions.

5) f(1) = 4; f(x) = 4; f(x) = 3 5) _______

A) B) C) D) Find the limit, if it exists.

6) Find:  for f(x) = -x + 1. 6) _______

A) 1 B) 0 C) -1 D) Does not exist

Solve the problem.

7) A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where Find P(x). 7) _______

A) 42 B) 105 C) 30 D) Does not exist

Use the given graph to find the indicated limit.

8) Find f(x). 8) _______

A) 4 B) -∞ C) ∞ D) 3

9) Find f(x). 9) _______

A) ∞ B) 4 C) 3 D) -∞

Find the limit.

10) Determine the limit. f(x), where f(x) = 10) ______

A) 0 B) -1 C) -∞ D) ∞

Provide an appropriate response.

11) If the limit at infinity exists, find the limit.  11) ______

A) ∞ B) 0 C) – D) – Use -∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.

12) g(x) = 12) ______

A) f(x) = ∞; f(x) = -∞; x = 6 is a vertical asymptote

B) f(x) = ∞; f(x) = -∞; x = 0 is a vertical asymptote

C) f(x) = -∞; f(x) = -∞; x = 6 is a vertical asymptote

D) f(x) = -∞; f(x) = ∞; x = 6 is a vertical asymptote

Provide an appropriate response.

13) Find the vertical asymptote(s) of the graph of the given function.

f(x) = 13) ______

A) y = 8 B) y = -3 C) x = -6 D) x = -8

14) Find the vertical asymptote(s) of the graph of the given function.

f(x) = 14) ______

A) y = 9, y = -3 B) x = 10, x = -10 C) x = 9, x = -3 D) x = -9

Solve the problem.

15) Suppose that the value V of a certain product decreases, or depreciates, with time t, in months, where

V(t) = 23 – .

Find V(t). 15) ______

A) 19 B) 23 C) 16 D) 7

Sketch a possible graph of a function that satisfies the given conditions.

16) f(0) = 6 and f(x) = 6 16) ______

A) B) C) D) The graph of y = f(x) is shown. Use the graph to answer the question.

17) Is f continuous at x = -1? 17) ______

A) Yes B) No

Provide an appropriate response.

18) Determine where the function is continuous. 18) ______

A) (-∞, -3) ∪ (-3, 2) ∪ (2, ∞) B) (-∞, -3) C) (-3, 2) ∪ (2, ∞) D) (-∞, -3) ∪ (-3, 2)

19) Determine where the function is continuous. 19) ______

A) B) ∪ C) D) (-∞, ∞)

20) Determine the x-values, if any, at which the function is discontinuous.

h(x) = 20) ______

A) -1, 0, 1 B) -1, 1 C) 1 D) None

21) Solve the inequality and express the answer in interval notation: 21) ______

A) (-5, ∞) B) (-5, 0) ∪ (4, ∞) C) (4, ∞) D) (-5, 0)

22) Use a sign chart to solve the inequality. Express answers in interval notation. > 16 22) ______

A) (-4, 4 ) B) (4, ∞) C) (-4, ∞) D) (-∞, -4) ∪ (4, ∞)

Solve the problem.

23) The cost of renting a snowblower is \$20 for the first hour (or any fraction thereof) and \$5 for each additional hour (or fraction thereof) up to a maximum rental time of 5 hours. Write a piecewise definition of the cost C(x) of renting a snowblower for x hours. Is C(x) continuous at x = 2.5?

23) ______

A) C(x) = ; Yes

B) C(x) = ; No

C) C(x) = ; No

D) C(x) = ; No

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