Applications of Differentiation

240 Chapter 3 Applications of Differentiation

3.9 Exercises See www.CalcChat.com for worked-out solutions to odd-numbered exercises.

x 1.9 1.99 2 2.01 2.1

f x

Tx

In Exercises 1–6, find the equation of the tangent line to the

graph of at the given point. Use this linear approximation to

complete the table.

1.

2.

3.

4.

5.

6.

In Exercises 7–10, use the information to evaluate and compare

and

7.

8.

9.

10.

In Exercises 11–20, find the differential of the given function.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

In Exercises 21–24, use differentials and the graph of to

approximate (a) and (b) To print an enlarged

copy of the graph, go to the website www.mathgraphs.com.

21. 22.

23. 24.

In Exercises 25 and 26, use differentials and the graph of to

approximate (a) and (b) given that

25. 26.

27. Area The measurement of the side of a square floor tile is

10 inches, with a possible error of inch. Use differentials to

approximate the possible propagated error in computing the

area of the square.

28. Area The measurements of the base and altitude of a triangle

are found to be 36 and 50 centimeters, respectively. The

possible error in each measurement is 0.25 centimeter. Use

differentials to approximate the possible propagated error in

computing the area of the triangle.

29. Area The measurement of the radius of the end of a log is

found to be 16 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.

30. Volume and Surface Area The measurement of the edge of a

cube is found to be 15 inches, with a possible error of 0.03 inch.

Use differentials to approximate the maximum possible

propagated error in computing (a) the volume of the cube and

(b) the surface area of the cube.

31. Area The measurement of a side of a square is found to be

12 centimeters, with a possible error of 0.05 centimeter.

(a) Approximate the percent error in computing the area of the

square.

(b) Estimate the maximum allowable percent error in measuring

the side if the error in computing the area cannot exceed

2.5%.

32. Circumference The measurement of the circumference of a

circle is found to be 64 centimeters, with a possible error of

0.9 centimeter.

(a) Approximate the percent error in computing the area of the

circle.

14

1

32

x

1 2 4

4

2

3

1

g′

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