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Question : A company estimates that the revenue (in dollars) from the sale of x units : 2151744

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

Find dy for the given values of x and Δx.

1) y = x^{3} + 2x; x = 2, Δx = 0.01

A) 0.14

B) 0.07

C) 0.007

D) 0.014

2) y = (1/x); x = 10, Δx = -0.003

A) 0.0003

B) 0.03

C) 0.003

D) 0.00003

3) y = (x^{2}/√(x^{2} + 21)); x = 10, Δx = 0.1

A) (142/1331)

B) (144/1331)

C) (148/1331)

D) (146/1331)

4) y = x^{3} - 4x^{2} + 2x + 1; x = 8, Δx = -0.3

A) -37

B) -39

C) 39

D) 37

5) y = 2x + 3; x = 18, Δx = 0.5

A) 0.1

B) 5

C) 1

D) 0.5

6) y = 5x^{2} - 2x + 3; x = 2, Δx = - (1/6)

A) -3

B) 3

C) 6

D) -6

7) y = 2x^{5} - 3x^{2} + x - 1; x = -1, Δx = (1/3)

A) (17/3)

B) (19/3)

C) (25/3)

D) (22/3)

8) y = (4/x^{4}) + 3√(x); x = 4, Δx = 0.5

A) (47/128)

B) .45

C) (45/128)

D) .47

9) y = (1/4x^{3}) + 3√(x^{2} + 3); x = 1, Δx = 0.2

A) 0.05

B) 0.15

C) 0.5

D) 0.02

10) y = (3x - 7/x - 1); x = 2, Δx = 0.1

A) 4

B) 6

C) 0.4

D) 0.6

Use the differential to approximate the quantity to four decimal places.

11) √(68)

A) 12.0000

B) 8.5000

C) 7.7500

D) 8.2500

12) √(16.28)

A) 3.9650

B) 4.2800

C) 4.0700

D) 4.0350

13) e^{0.39}

A) .6100

B) 1.477

C) 1.3900

D) 0.6771

14) e^{0.156}

A) .8440

B) 0.8556

C) 1.1688

D) 1.1560

15) ln1.02

A) -0.0203

B) 0.0198

C) -0.0200

D) 0.0200

Solve the problem.

16) A company estimates that the revenue (in dollars) from the sale of x units of dog houses is given by C(x) = 760 +0.02x + 0.0002x^{2}. Use the differential to approximate the change in revenue from the sale of one more dog house when 510 dog houses are sold.

A) $53.00

B) $0.22

C) $0.53

D) $22.00

17) A grocery store estimates that the revenue (in dollars) from the sale of x cases of condensed soup is given by R(x) = -5600 + 9.3x - 0.0017x^{2}. Use the differential to approximate the change in revenue from the sale of one more case of soup when 1000 cases are sold.

A) $5.90

B) -$7.60

C) $2000.00

D) $7.60

18) The concentration of a certain drug in the bloodstream x hours after being administered is approximately C(x) = (6x/14 + x^{2}). Use the differential to approximate the change in concentration as x changes from 1 to 1.4.

A) 0.50

B) 0.24

C) 0.14

D) 0.25

19) A tumor is approximately spherical in shape. If the radius of the tumor changes from 8 mm to 11 mm, find the approximate change in volume. Round your answer to the nearest hundred.

A) 2100 mm^{3}

B) 3700 mm^{3}

C) 300 mm^{3}

D) 2400 mm^{3}

20) The weight of a ram can be estimated by the function W(t) = -7.3 + 304.8e^{-e}^^{(-0.00956(t - 131.9)},

where t is the age of the ram (in days) and W(t) is the weight of the ram (in kg). If a particular ram is 90 days old, use differentials to estimate how much weight it will gain before it is 120 days old.

A) 29.3 kg

B) 31.9 kg

C) 16.4 kg

D) 30.9 kg

21) The edge of a square is measured as 5.22 inches, with a possible error of ±0.05 inch. Estimate the maximum error in the area of the square.

A) 0.261 in^{2}

B) 0.1 in^{2}

C) 0.0025 in^{2}

D) 0.522 in^{2}

22) A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from 5.6 cm to 5.8 cm.

A) 234.15 cm^{3}

B) 25.088π cm^{3}

C) 0.896π cm^{3}

D) 125.44π cm^{3}