CALCULUS

MTH 135 – Homework Assignment Week 1 January 10, 2022

 

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Name___________________________________

 

 

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

 

Provide an appropriate response.

1) Given that f(x) = (x/7 - x), find f(- (4/5)). Express the answer as a simplified fraction. 1) _______

 

A) – (4/39) B) (39/4) C) – (39/4) D) (4/39)

 

 

Use the graph to evaluate the indicated limit and function value or state that it does not exist.

 

2) Find (x→0) is under (lim)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: (x→-1) is under (lim) (6x + 5/5x - 6) 3) _______

 

A) -11 B) (1/11) C) 1 D) – (1/11)

 

 

4) Given(x→4) is under (lim)f(x) = -2 and(x→4) is under (lim) g(x) = 5, find(x→4) is under (lim) ([g(x) - f(x)]/- 4 f(x)). 4) _______

 

A) – (3/8) B) – (7/8) C) (3/8) D) (7/8)

 

 

 

 

 

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

 

5) f(1) = 4; (x→(1) with superscript (-)) is under (lim)f(x) = 4; (x→(1) with superscript (+)) is under (lim)f(x) = 3

 

 5) _______

 

 

A)

 

B)

 

C)

 

D)

 

 

 

Find the limit, if it exists.

 

6) Find: (h→0) is under (lim) (f(7 + h) - f(7)/h) 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 P(x) = (90 + 60x/x + 5). Find (x→5) is under (lim)P(x). 7) _______

 

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

 

 

 

Use the given graph to find the indicated limit.

 

8)

Find(x→ ∞) is under (lim)f(x). 8) _______

 

A) 4 B) -∞ C) ∞ D) 3

 

 

9)

Find(x→ -∞) is under (lim)f(x). 9) _______

 

A) ∞ B) 4 C) 3 D) -∞

 

 

 

Find the limit.

 

10) Determine the limit.

(x → - (10) with superscript ( -)) is under (lim)f(x), where f(x) = (1/x + 10)

10) ______

 

A) 0 B) -1 C) -∞ D) ∞

 

Provide an appropriate response.

 

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

(x → ∞) is under (lim) (5(x) with superscript (2) + 7x - 9/- 6(x) with superscript (2) + 2) 11) ______

 

A) ∞ B) 0 C) – (5/6) D) – (2/9)

 

 

Use -∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.

 

12) g(x) = (x/6 - x) 12) ______

 

A) (x → (6) with superscript (-)) is under (lim)f(x) = ∞; (x → (6) with superscript (+)) is under (lim)f(x) = -∞; x = 6 is a vertical asymptote

B) (x → (6) with superscript (-)) is under (lim)f(x) = ∞; (x → (6) with superscript (+)) is under (lim)f(x) = -∞; x = 0 is a vertical asymptote

C) (x → (6) with superscript (-)) is under (lim)f(x) = -∞; (x → (6) with superscript (+)) is under (lim)f(x) = -∞; x = 6 is a vertical asymptote

D) (x → (6) with superscript (-)) is under (lim)f(x) = -∞; (x → (6) with superscript (+)) is under (lim)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) = (3x - 9/5x + 30) 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) = ((x) with superscript (2) - 100/(x - 9)(x + 3)) 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 – (16(t) with superscript (2)/((t + 2)) with superscript ( 2)).

Find (t→∞) is under (lim)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 (x → 0) is under (lim)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 H(x) = ((x) with superscript (2) + 7/(x) with superscript (2) + x - 6) is continuous. 18) ______

 

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

 

 

19) Determine where the function f(x) = (5x/2x - 3) is continuous. 19) ______

 

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

 

 

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

h(x) = {table ( ((x) with superscript (2) - 9       for  x < -1)(0               for  -1 ≤ x ≤ 1)((x) with superscript (2) + 9      for  x > 1) ) 20) ______

 

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

 

21) Solve the inequality and express the answer in interval notation: ((x) with superscript (2) - 4x/x + 5) > 0. 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.

 

(x) with superscript (2) > 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) = table ( (20 if 0 < x ≤ 1)(25 if 1 < x ≤ 2)(30 if 2 < x ≤ 3)(35 if 3 < x ≤ 4)(40 if 4 < x ≤ 5) ); Yes

 

B) C(x) = table ( (20 if 0 < x ≤ 1)(25 if 1 < x ≤ 2)(30 if 2 < x ≤ 3)(35 if 3 < x ≤ 4)(40 if 4 < x ≤ 5) ); No

 

C) C(x) = table ( (20 if 0 ≤ x ≤ 1)(25 if 1 ≤ x ≤ 2)(30 if 2 ≤ x ≤ 3)(35 if 3 ≤ x ≤ 4)(40 if 4 ≤ x ≤ 5) ); No

 

D) C(x) = table ( (25 if 0 < x ≤ 1)(30 if 1 < x ≤ 2)(35 if 2 < x ≤ 3)(40 if 3 < x ≤ 4)(45 if 4 < x ≤ 5) ); No

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