Deck 13: Section 4: Functions of Several Variables

Question 1

Suppose a triangle is measured and two adjacent sides are found to be 5 inches and 7 inches long, with an included angle of . The possible errors in measurement are inch for the sides and 0.02 radian for the angle. Approximate the maximum possible error in the computation of the area. Round your answer to two decimal places.

A)
B)
C)
D)
E)

Answer 1

Question 2

Given , use the total differential to approximate at towards . Round your answer to two decimal places.

A) 10.96
B) -6.04
C) 49.96
D) 31.92
E) 33.92

Answer 2

10.96

Question 3

Suppose electrical power P is given by , where E is voltage and R is resistance. Approximate the maximum percent error in calculating the power if 140 volts are applied to a 3000-ohm resistor and the possible percent errors in measuring E and R are 5% and 8%, respectively.

A) 24%
B) 42%
C) 38%
D) 43%
E) 18%

Answer 3

18%

Question 4

Suppose the period T of a pendulum of length L is where g is the acceleration due to gravity. A pendulum is moved from the Canal Zone, where feet per second per second, to Greenland, where feet per second per second. Because of the change in temperature, the length of the pendulum changes from 2.6 feet to 2.45 feet. Approximate the change in the period of the pendulum. Round your answer to four decimal places.

A) 5.8508 seconds
B) -0.0746 second
C) 0.9254 second
D) 7.9254 seconds
E) -7.1492 seconds

Question 5

Given , calculate by evaluating and . Round your answer to four decimal places.

A) -7.9441
B) -45.9441
C) -19.9441
D) 0.1118
E) -4.8882

Question 6

Find the total differential for the function .

A)
B)
C)
D)
E)

Question 7

Find and use the total differential to approximate the quantity . Round your answer to two decimal places.

A) 5.80
B) 2.80
C) 4.40
D) 2.40
E) 0.40

Question 8

Find the total differential of the function .

A)
B)
C)
D)
E)

Question 9

Given , calculate by evaluating and . Round your answer to four decimal places.

A) 7.3037
B) 5.6074
C) -16.6963
D) -2.6963
E) -21.3926

Question 10

Given , use the total differential to approximate at towards . Round your answer to four decimal places.

A) -35.7266
B) 30.5500
C) 17.2734
D) 15.5468
E) -4.7266

Question 11

Find the total differential for the function .

A)
B)
C)
D)
E)

Question 12

Suppose the formula for wind chill C (in degrees Fahrenheit) is given by where v is the wind speed in miles per hour and T is the temperature in degrees Fahrenheit. The wind speed is miles per hour and the temperature is Fahrenheit. Use to estimate the maximum possible propagated error in calculating the wind chill. Round your answer to four decimal places.

A)
B)
C)
D)
E)

Question 13

Find the total differential of the function .

A)
B)
C)
D)
E)

Question 14

The radius r and height h of a right circular cylinder are measured with possible errors of 5% and 1%, respectively. Approximate the maximum possible percent error in measuring the volume.

A) 18 %
B) 11 %
C) 24 %
D) 12 %
E) 7 %

Question 15

Find the total differential of the function .

A)
B)
C)
D)
E)

Question 16

Suppose the centripetal acceleration of a particle moving in a circle is , where v is the velocity and r is the radius of the circle. Approximate the maximum percent error in measuring the acceleration due to errors of 4% in v and 2% in r.

A) 11%
B) 16%
C) 10%
D) 21%
E) 13%

Question 17

Suppose the formula for wind chill C (in degrees Fahrenheit) is given by where v is the wind speed in miles per hour and T is the temperature in degrees Fahrenheit. The wind speed is miles per hour and the temperature is Fahrenheit. Use to estimate the relative error in calculating the wind chill. Round your answer to two decimal places.

A)
B)
C)
D)
E)