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Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value

Question : Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value : 2151555

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

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.

1) (x2 - 100/x - 10)

A) 20

B) 1

C) 10

D) Does not exist

2) (x2 + 5x + 6/x + 3)

A) Does not exist

B) -1

C) 5

D) 30

3) (x2 + 8x - 9/x - 1)

A) 10

B) 8

C) Does not exist

D) 0

4) (x2 + 2x - 80/x2 - 64)

A) (9/8)

B) -(1/8)

C) 0

D) Does not exist

5) (x2 - 9/x2 - 4x + 3)

A) 3

B) Does not exist

C) (3/2)

D) 0

6) ((1/x + 6) -(1/6)/x)

A) -(1/36)

B) (1/36)

C) Does not exist

D) 0

7) (x2 - 4/x + 2)

A) -2

B) Does not exist

C) -4

D) 0

8) (x2 + 12x + 32/x + 4)

A) Does not exist

B) 4

C) 12

D) 96

9) (√(x) - 8/x - 64)

A) 8

B) (1/16)

C) (1/8)

D) 0

10) ((x + h)3 - x3/h)

A) 0

B) 3x2

C) 3x2 + 3xh + h2

D) Does not exist

11) (-5x2 + 9x - 2/-3x2 + 1)

A) -(1/2)

B) 0

C) ∞

D) (5/3)

12) (-3x3 + 5x/5x4 + 4x3 + 4)

A) 0

B) ∞

C) -(3/5)

D) 1

13) (x/4x - 10)

A) 0

B) (1/4)

C) ∞

D) -(1/4)

14) (2x + 1/15x - 7 )

A) -(1/7)

B) ∞

C) 0

D) (2/15)

15) 4x + 1/8x2 - 7 )

A) -(1/7)

B) 0

C) ∞

D) (1/2)

16) (5x6 - x + 5/7x2 - x - 7)

A) ∞

B) -∞

C) (5/7)

D) Does not exist

17) (6x2 + 5x - 4x6/6x2 - 5x + 3)

A) -∞

B) Does not exist

C) 1

D) ∞

Use the properties of limits to help decide whether each limit exits. If a limit exists, find its value.

18) Let f(x) = {(x2 - 1 if x < 0)

(1 if x ≥ 0). Findf(x).

A) Does not exist

B) -1

C) 0

D) 1

19) Let f(x) = {(7x - 6 if x ≤ 1)

(4x - 3 if x > 1). Findf(x).

A) -6

B) Does not exist

C) 1

D) -3

20)

Let f(x) = {(-3x - 2 if x < 1)

(1 if x = 1)

(2x + 1 if x > 1). Findf(x).

A) -5

B) Does not exist

C) 0

D) 3

Use a graphing utility to find the limit, if it exists.

21) (x4 - 3x3 + 5x2 - 8x + 5/x - 1)

A) -2

B) 1

C) Does not exist.

D) -3

22) ((5 + 3x2/3 + 7x4/3)3/x4)

A) 7.5

B) Does not exist.

C) 7

D) 343

23) (x2 - 49/x - 7)

A) 1

B) Does not exist

C) 7

D) 14

24) (x2 + 4x - 21/x2 - 9)

A) -(2/3)

B) Does not exist

C) 0

D) (5/3)

25) (x2 - 16/x2 - 9x + 20)

A) - 8

B) Does not exist

C) - 4

D) 0

26) (√(64t2 - 512) /t - 8 )

A) 8

B) 512

C) Does not exist

D) 64

27) (x4 + 3x - 4/x2 - 1)

A) ∞

B) Does not exist

C) 1

D) 3.5

28) (√(16x2 + 6)/3x)

A) 0

B) Does not exist

C) 1.333

D) -1.333

29) (√(49x2 + 6x + 5)/2x)

A) -3.5

B) Does not exist

C) 3.5

D) ∞

Solve the problem.

30) A company training program determines that, on average, a new employee can do P(s) pieces of work per day after s days of on-the-job training, where P(s) = (90 + 50s/s + 7). Find P(s).

A) 56

B) 30

C) 65

D) Does not exist

31) The cost of manufacturing a particular videotape is c(x) = 15,000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by overbar(c)(x), is found by dividing c(x) by x. Find  overbar(c)(x).

A) 8

B) Does not exist

C) 14

D) 20

32) Given is a graph of a portion of the postage function, which depicts the cost(in cents) of mailing a letter, p, versus the weight(in ounces) of the letter, x. Find each limit, if it exists:

p(x), p(x), p(x)

A) 99; 77; does not exist

B) 77; 77; 77

C) 77; 99; 77

D) 77; 99; does not exist

33) Suppose that the cost, p, of shipping a 3-pound parcel depends on the distance shipped, x, according to the function p(x) depicted in the graph. Find each limit, if it exists:

p(x), p(x), p(x)

A) 5; 10; 15

B) 5; does not exist; does not exist

C) 5; 5; 15

D) 5; does not exist; 15

34) Suppose the the cost, C, of producing x units of a product can be illustrated by the given graph. Find each limit, if it exists:

p(x), p(x), p(x)

A) 200; does not exist; does not exist

B) 200; 200; 200

C) 200; 300; 200

D) 200; 300; does not exist

35) Suppose that the unit price, p, for x units of a product can be illustrated by the given graph. Find each limit, if it exists:

p(x), p(x), p(x), p(x)

A) 10; 8; 8; 8

B) 10; 8; does not exist; 8

C) 8; 8; does not exist; 8

D) 8; 8; 8; 8

36) The blood alcohol level h hours after consumption of 2 ounces of pure ethanol is given by C(h) =(0.55h/h3 - h2 + 5). Find the blood alcohol level as h approaches infinity.

A) .55

B) ∞

C) .11

D) 0

37) The current value of an annuity per period is given by P =(R/i) -(R/i(1 + i)n) , where n is the number of periods, i is the interest rate, and R is the amount of the periodic payment. Find the limit of the current value equation as n approaches infinity to derive an expression for the current value for an annuity that makes payments in perpetuity.

A) P = ∞

B) P = 0

C) P =(R/i)

D) P =(R/i) - R

Solution
5 (1 Ratings )

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Calculus 3 Months Ago 30 Views
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