3.9 Differentials 225
3.9 Differentials
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 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.
226 Chapter 3: Applications of Differentiation
____ 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.
3.9 Differentials 227
____ 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.
228 Chapter 3: Applications of Differentiation
____ 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
3.9 Differentials 229
3.9 Differentials
Answer Section