Larson_Calculus_10e ch13sec04
MULTIPLE CHOICE
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.
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
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 %
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%
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