Larson_Calculus_10e ch03sec09
MULTIPLE CHOICE
1. Find the equation of the tangent line T to the graph of at the given point
a.
b.
c.
d.
e.
2. Find the equation of the tangent line T to the graph of at the given point
a.
b.
c.
d.
e.
3. Compare dy and for at x = –1 with Give your answers to four
decimal places.
a.
b.
c.
d.
e.
4. Compare dy and for at x = 0 with Give your answers to four decimal
places.
a.
b.
c.
d.
e.
5. Find the differential dy of the function
a.
b.
c.
d.
e.
6. Find the differential dy of the function .
a.
b.
c.
d.
e.
7. Find the differential dy of the function .
a.
b.
c.
d.
e.
8. The measurement of the side of a square floor tile is 14 inches, with a possible error of inch. Use
differentials to approximate the possible propagated error in computing the area of the square.
a.
b.
c.
d.
e.
9. The measurements of the base and altitude of a triangle are found to be 54 and 33 centimeters. The
possible error in each measurement is 0.25 centimeter. Use differentials to estimate the propagated
error in computing the area of the triangle. Round your answer to four decimal places.
a.
b.
c.
d.
e.
10. The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of
inch. Use differentials to approximate the possible propagated error in computing the area of the end of
the log.
a.
b.
c.
d.
e.
11. The radius of a spherical balloon is measured to be 8 inches, with a possible error of 0.03 inch. Use
differentials to approximate the maximum possible error in calculating the volume of the sphere.
Round your answer to two decimal places.
a.
b.
c.
d.
e.
12. The radius of a spherical balloon is measured to be 12 inches, with a possible error of 0.06 inch. Use
differentials to approximate the maximum possible error in calculating the surface area of the sphere.
Round your answer to two decimal places.
a.
b.
c.
d.
e.
13. The range R of a projectile is where is the initial velocity in feet per second and
is the angle of elevation. If feet per second and is changed from to use
differentials to approximate the change in the range. Round your answer to the nearest integer.
a.
2,593 ft
b.
4,568 ft
c.
5,623 ft
d.
2,811 ft
e.
5,186 ft
14. Use differentials to approximate the value of . Round your answer to four decimal places.
a.
5.0000
b.
5.0100
c.
5.0400
d.
5.0200
e.
5.0300
15. Use differentials to approximate the value of . Round your answer to four decimal places.
a.
1.9683
b.
1.9483
c.
1.9383
d.
1.9583
e.
1.9783