768 Chapter 13: Functions of Several Variables
13.4 Differentials
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the total differential of the function .
a.
b.
c.
d.
e.
____ 2. Find the total differential of the function .
a.
b.
c.
d.
e.
13.4 Differentials 769
____ 3. Find the total differential for the function .
a.
b.
c.
d.
e.
____ 4. Find the total differential for the function .
a.
b.
c.
d.
e.
____ 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
____ 6. 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
770 Chapter 13: Functions of Several Variables
____ 7. 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
____ 8. 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
____ 9. 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
____ 10. 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 %
13.4 Differentials 771
____ 11. 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.
____ 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 relative error in calculating the wind chill. Round your
answer to two decimal places.
a.
b.
c.
d.
e.
____ 13. 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%
772 Chapter 13: Functions of Several Variables
____ 14. 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%
____ 15. 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
13.4 Differentials 773
13.4 Differentials
Answer Section
MULTIPLE CHOICE