### Sample Chapter

###### SAMPLE QUESTIONS

Stewart_Essential Calc_2ET ch01sec02

MULTIPLE CHOICE

1. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

What is the F-intercept and what does it represent?

 a. 0, Fahrenheit temperature corresponding to b. , Fahrenheit temperature corresponding to c. , Celsius temperature corresponding to d. 32, Celsius temperature corresponding to e. 32, Fahrenheit temperature corresponding to

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    1.2.9b

MSC:   Bimodal          NOT:   Section 1.2

1. The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her  to drive  mi and in July it cost her  to drive  mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

 a. b. c. d. e.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    1.2.14a

MSC:   Bimodal          NOT:   Section 1.2

1. Many physical quantities are connected by inverse square laws, that is, by power functions of the form

.

In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move

the distance to the lamp. How much brighter is the light?

 a. times b. times c. times d. times e. times

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    1.2.15

MSC:   Bimodal          NOT:   Section 1.2

NUMERIC RESPONSE

1. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

Complete the table and find the slope.

ANS:   ; slope =

PTS:    1                      DIF:    Medium          REF:    1.2.9a

MSC:   Numerical Response                           NOT:   Section 1.2

1. It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in  of the caves by the equation

(a) The cave called mission impossible near puebla, mexico, has suface area of .

How many species of bats would expect to find in that cave?

(b) If you discover that  species of bats live in cave estimate the area of the cave.

ANS:

1. a) species
2. b)

PTS:    1                      DIF:    Medium          REF:    1.2.16

MSC:   Numerical Response                           NOT:   Section 1.2

Stewart_Essential Calc_2ET ch02sec02

MULTIPLE CHOICE

1. If find the domain of

 a. b. c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    2.2.21

MSC:   Bimodal          NOT:   Section 2.2

1. If find the defination of derivative to find

 a. b. c. d. e. None of these

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    2.2.23

MSC:   Bimodal          NOT:   Section 2.2

1. Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative.

 a. b. c. d. e.

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    2.2.27

MSC:   Bimodal          NOT:   Section 2.2

1. If , find .

 a. b. c. d. e.

ANS:   C                     PTS:    1                      DIF:    Easy                REF:    2.2.29a

MSC:   Bimodal          NOT:   Section 2.2

1. If , find .

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Easy                REF:    2.2.30a

MSC:   Bimodal          NOT:   Section 2.2

Stewart_Essential Calc_2ET ch03sec02

MULTIPLE CHOICE

1. Find a formula for the inverse of the function.

 a. b. c. d. e.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    3.2.25

MSC:   Bimodal          NOT:   Section 3.2

1. Find the exact value of the expression.

 a. 2 b. 4 c. 1 d. 5 e. 3

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    3.2.45a

MSC:   Bimodal          NOT:   Section 3.2

1. Use the laws of logarithms to expand the expression.

ln

 a. ln b. ln (x + 5) –  ln (x – 6) c. ln [(x + 5)(x – 6)] d. ln

ANS:   B                     PTS:    1                      DIF:    Easy                REF:    3.2.48

MSC:   Bimodal          NOT:   Section 3.2

1. Use the laws of logarithms to write the expression as the logarithm of a single quantity.

4 ln 5 – ln (x + 6)

 a. b. c. d.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    3.2.53

MSC:   Bimodal          NOT:   Section 3.2

1. Suppose that the graph of  is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft? Rounded to the nearest mile.

 a. 13,014,952 mi b. 13015052.4 mi c. 5.2 mi d. 13,015,152 mi e. 1084587.7 mi

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    3.2.57

MSC:   Bimodal          NOT:   Section 3.2

1. Solve the equation.

 a. x = ln  + 2 b. x = ln  – 2 c. x = ln  + 2 d. x = ln  – 2

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    3.2.63

MSC:   Bimodal          NOT:   Section 3.2

1. When a camera flash goes off, the batteries immediately begin to recharge the flash’s capacitor, which stores electric charge given by

(The maximum charge capacity  is and t is measured in seconds.) How long does it take to recharge the capacitor to 90% of capacity if ?

 a. seconds b. seconds c. seconds d. seconds e. seconds

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    3.2.78b

MSC:   Bimodal          NOT:   Section 3.2

NUMERIC RESPONSE

1. Find the domain, range, and x-intercept(s) of the function.

ANS:

Domain:

Range:

x-intercept:

PTS:    1                      DIF:    Medium          REF:    3.2.62

MSC:   Numerical Response                           NOT:   Section 3.2

1. Solve each equation for x.

(a)     (b)

ANS:   ,

PTS:    1                      DIF:    Medium          REF:    3.2.64

MSC:   Numerical Response                           NOT:   Section 3.2

1. Determine whether  f  is one-to-one.

ANS:

Yes

PTS:    1                      DIF:    Easy                REF:    3.2.8                MSC:   Short Answer

NOT:   Section 3.2

1. The graph of  f  is given. Sketch the graph of   on the same set of axes.

3

ANS:

PTS:    1                      DIF:    Easy                REF:    3.2.30              MSC:   Short Answer

NOT:   Section 3.2

Stewart_Essential Calc_2ET ch04sec02

MULTIPLE CHOICE

1. The function  satisfies the hypotheses of Rolle’s Theorem on the interval .  Find all values of c that satisfy the conclusion of the theorem.

 a. b. c. d.

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    4.2.1

MSC:   Bimodal          NOT:   Section 4.2

1. Verify that the function satisfies the three hypotheses of Rolle’s Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.

 a. b. c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    4.2.2

MSC:   Bimodal          NOT:   Section 4.2

1. Verify that the function satisfies the three hypotheses of Rolle’s Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.

,

 a. None of these b. , c. , d. , e. ,

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    4.2.4

MSC:   Bimodal          NOT:   Section 4.2

1. The function  satisfies the hypotheses of Rolle’s Theorem on the interval .  Find all values of c that satisfy the conclusion of the theorem.

 a. –6, –4 b. –5, –4 c. –6 d. –5

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    4.2.9

MSC:   Bimodal          NOT:   Section 4.2

1. The function  satisfies the hypotheses of the Mean Value Theorem on the interval .  Find all values of c that satisfy the conclusion of the theorem.

 a. –7 b. –8, –6 c. –8, –7 d. –6

ANS:   A                     PTS:    1                      DIF:    Easy                REF:    4.2.10

MSC:   Bimodal          NOT:   Section 4.2

1. Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval.

,

 a. b. c. d. e. None of these

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    4.2.13

MSC:   Bimodal          NOT:   Section 4.2

MULTIPLE RESPONSE

1. Use the graph of  to estimate the values of c that satisfy the conclusion of the Mean Value Theorem for the interval [0, 7].

Select all that apply.

 a. b. c. d. e. f. g. h.

ANS:   A, C, D, E       PTS:    1                      DIF:    Medium          REF:    4.2.7

MSC:   Multiple Response                              NOT:   Section 4.2

NUMERIC RESPONSE

1. At 4:00 P.M. a car’s speedometer reads 25 . At 4:15 it reads 72 . At some time between 4:00 and 4:15 the acceleration is exactly x . Find x.

ANS:

PTS:    1                      DIF:    Medium          REF:    4.2.34

MSC:   Numerical Response                           NOT:   Section 4.2

Stewart_Essential Calc_2ET ch05sec02

MULTIPLE CHOICE

1. Evaluate the Riemann sum for  with four subintervals, taking the sample points to be right endpoints.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    5.2.1

MSC:   Bimodal          NOT:   Section 5.2

1. Use the Midpoint Rule with n = 5 to approximate the integral.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    5.2.11

MSC:   Bimodal          NOT:   Section 5.2

1. Use the Midpoint Rule with n = 10 to approximate the integral.

 a. b. c. d. e.

ANS:   D                     PTS:    1                      DIF:    Medium          REF:    5.2.13

MSC:   Bimodal          NOT:   Section 5.2

1. If  and , find .

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    5.2.40

MSC:   Bimodal          NOT:   Section 5.2

NUMERIC RESPONSE

1. A table of values of an increasing function  is shown. Use the table to find an upper estimate of

.

 –45 –37 –27 9 10 23

ANS:   –110

PTS:    1                      DIF:    Medium          REF:    5.2.9

MSC:   Numerical Response                           NOT:   Section 5.2

1. Express the integral as a limit of sums. Then evaluate the limit.

ANS:

PTS:    1                      DIF:    Medium          REF:    5.2.27

MSC:   Numerical Response                           NOT:   Section 5.2

1. Evaluate by interpreting it in terms of areas.

ANS:

PTS:    1                      DIF:    Medium          REF:    5.2.31

MSC:   Numerical Response                           NOT:   Section 5.2

1. Evaluate by interpreting it in terms of areas.

ANS:

PTS:    1                      DIF:    Medium          REF:    5.2.33

MSC:   Numerical Response                           NOT:   Section 5.2

1. Evaluate by interpreting it in terms of areas.

ANS:

PTS:    1                      DIF:    Medium          REF:    5.2.34

MSC:   Numerical Response                           NOT:   Section 5.2

1. Given that , find .

ANS:

PTS:    1                      DIF:    Medium          REF:    5.2.38

MSC:   Numerical Response                           NOT:   Section 5.2

Stewart_Essential Calc_2ET ch06sec02

MULTIPLE CHOICE

1. Find the integral.

 a. b. c. d.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    6.2.2

MSC:   Bimodal          NOT:   Section 6.2

1. Evaluate the integral.

 a. b. c. d.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    6.2.5

MSC:   Bimodal          NOT:   Section 6.2

1. Find the integral.

 a. b. c. d.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    6.2.14

MSC:   Bimodal          NOT:   Section 6.2

1. Find the integral.

 a. b. c. d.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    6.2.17

MSC:   Bimodal          NOT:   Section 6.2

1. Find the integral.

 a. b. c. d.

ANS:   D                     PTS:    1                      DIF:    Medium          REF:    6.2.18

MSC:   Bimodal          NOT:   Section 6.2

1. Evaluate the integral.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    6.2.35

MSC:   Bimodal          NOT:   Section 6.2

1. A particle moves on a straight line with velocity function . Find its position function .

 a. b. c. d. e.

ANS:   D                     PTS:    1                      DIF:    Medium          REF:    6.2.40

MSC:   Bimodal          NOT:   Section 6.2

1. Evaluate the integral using the indicated trigonometric substitution.

 a. b. c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    6.2.46

MSC:   Bimodal          NOT:   Section 6.2

1. Find the integral using an appropriate trigonometric substitution.

 a. b. c. d.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    6.2.55

MSC:   Bimodal          NOT:   Section 6.2

1. Find the integral using an appropriate trigonometric substitution.

 a. b. c. d.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    6.2.65

MSC:   Bimodal          NOT:   Section 6.2

NUMERIC RESPONSE

1. Household electricity is supplied in the form of alternating current that varies from 170 V to –170 V with a frequency of 60 cycles per second (Hz). The voltage is thus given by the function E(t), where t is the time in seconds. Voltmeters read the RMS (root-mean-square) voltage, which is the square root of the average value of  over one cycle. Calculate the RMS voltage of household current. Round your answer to the nearest integer.

ANS:

PTS:    1                      DIF:    Medium          REF:    6.2.39

MSC:   Numerical Response                           NOT:   Section 6.2

1. Evaluate the integral using the indicated trigonometric substitution.

ANS:

PTS:    1                      DIF:    Medium          REF:    6.2.66

MSC:   Numerical Response                           NOT:   Section 6.2

1. Find the area of the region bounded by the hyperbola  and the line .

ANS:

PTS:    1                      DIF:    Medium          REF:    6.2.68

MSC:   Numerical Response                           NOT:   Section 6.2

1. Find the integral.

ANS:

PTS:    1                      DIF:    Medium          REF:    6.2.32              MSC:   Short Answer

NOT:   Section 6.2

Stewart_Essential Calc_2ET ch07sec02

MULTIPLE CHOICE

1. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

 a. b. c. d. e. None

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    7.2.4

MSC:   Bimodal          NOT:   Section 7.2

1. Find the volume of the solid obtained by rotating the region bounded by  about the x-axis.

 a. b. c. d. e.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    7.2.5

MSC:   Bimodal          NOT:   Section 7.2

1. Find the volume of the solid obtained by rotating the region bounded by  about the line

 a. b. c. d. e.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    7.2.9

MSC:   Bimodal          NOT:   Section 7.2

1. Find the volume of a pyramid with height  and base an equilateral triangle with side a = .

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    7.2.36

MSC:   Bimodal          NOT:   Section 7.2

NUMERIC RESPONSE

1. Find the volume of the solid obtained by rotating the region bounded by   and  about the y-axis.

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.7

MSC:   Numerical Response                           NOT:   Section 7.2

1. Find the volume of the solid obtained by rotating the region bounded by   and  about the line

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.12

MSC:   Numerical Response                           NOT:   Section 7.2

1. Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.26

MSC:   Numerical Response                           NOT:   Section 7.2

1. Find the volume of a cap of a sphere with radius r =  and height h = 3.

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.33

MSC:   Numerical Response                           NOT:   Section 7.2

1. Find the volume of the frustum of a pyramid with square base of side  square top of side  and height

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.34

MSC:   Numerical Response                           NOT:   Section 7.2

1. The base of S is a circular region with boundary curve  Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base.

Find the volume of S.

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.39

MSC:   Numerical Response                           NOT:   Section 7.2

1. The base of S is the parabolic region  Cross-sections perpendicular to the y axis are squares.

Find the volume of S.

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.42

MSC:   Numerical Response                           NOT:   Section 7.2

1. True or False?

The volume of a solid torus (the donut-shaped solid shown in the figure) with r =  and R =  is

ANS:   True

PTS:    1                      DIF:    Medium          REF:    7.2.47

MSC:   Numerical Response                           NOT:   Section 7.2

1. Find the volume common to two spheres, each with radius r =  if the center of each sphere lies on the surface of the other sphere.

ANS:

PTS:    1                      DIF:    Medium          REF:    7.2.51

MSC:   Numerical Response                           NOT:   Section 7.2

Stewart_Essential Calc_2ET ch08sec02

MULTIPLE CHOICE

1. Determine whether the given series converges or diverges. If it converges, find its sum.

 a. b. Diverges c. d.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    8.2.14

MSC:   Bimodal          NOT:   Section 8.2

1. Determine whether the given series converges or diverges. If it converges, find its sum.

 a. b. Diverges c. 1 d.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    8.2.16

MSC:   Bimodal          NOT:   Section 8.2

1. Determine whether the geometric series converges or diverges. If it converges, find its sum.

 a. b. c. d. Diverges

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    8.2.23

MSC:   Bimodal          NOT:   Section 8.2

1. Determine whether the series is convergent or divergent by expressing  as a telescoping sum. If it is convergent, find its sum.

.

 a. b. diverges c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    8.2.25

MSC:   Bimodal          NOT:   Section 8.2

1. Determine whether the series is convergent or divergent by expressing  as a telescoping sum. If it is convergent, find its sum.

.

 a. diverges b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    8.2.27

MSC:   Bimodal          NOT:   Section 8.2

1. When money is spent on goods and services, those that receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the local government begins the process by spending D dollars. Suppose that each recipient of spent money spends  and saves  of the money that he or she receives. The values c and s are called the marginal propensity to consume and the marginal propensity to save and, of course, .

The number k = 1/s is called the multiplier. What is the multiplier if the marginal propensity to consume is ?

 a. 4 b. 6 c. 3 d. 7 e. 2.5

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    8.2.43b

MSC:   Bimodal          NOT:   Section 8.2

NUMERIC RESPONSE

1. Express the number  as a ratio of integers.

ANS:

PTS:    1                      DIF:    Medium          REF:    8.2.32

MSC:   Numerical Response                           NOT:   Section 8.2

1. A right triangle ABC is given with  and . CD is drawn perpendicular to AB, DE is drawn perpendicular to BC, EF  AB and this process is continued indefinitely as shown in the figure. Find the total length of all the perpendiculars

ANS:

PTS:    1                      DIF:    Medium          REF:    8.2.48

MSC:   Numerical Response                           NOT:   Section 8.2

1. A sequenceis  defined recursively by the equation  for  where . Use your calculator to guess the limit of the sequence.

ANS:

PTS:    1                      DIF:    Medium          REF:    8.2.58a

MSC:   Numerical Response                           NOT:   Section 8.2

1. Determine whether the given series converges or diverges. If it converges, find its sum.

ANS:

PTS:    1                      DIF:    Medium          REF:    8.2.17              MSC:   Short Answer

NOT:   Section 8.2

1. Express the number as a rational number.

ANS:

PTS:    1                      DIF:    Medium          REF:    8.2.33              MSC:   Short Answer

NOT:   Section 8.2

Stewart_Essential Calc_2ET ch09sec02

MULTIPLE CHOICE

1. Find the point(s) on the curve where the tangent is horizontal.

 a. b. c. d. e. None of these

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    9.2.13

MSC:   Bimodal          NOT:   Section 9.2

1. Find the length of the curve.

, ,

 a. b. c. d. e. None of these

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    9.2.37

MSC:   Bimodal          NOT:   Section 9.2

NUMERIC RESPONSE

1. Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

ANS:

PTS:    1                      DIF:    Medium          REF:    9.2.34

MSC:   Numerical Response                           NOT:   Section 9.2

1. Set up, but do not evaluate, an integral that represents the length of the parametric curve.

ANS:

PTS:    1                      DIF:    Medium          REF:    9.2.35

MSC:   Numerical Response                           NOT:   Section 9.2

1. Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

ANS:

PTS:    1                      DIF:    Medium          REF:    9.2.54

MSC:   Numerical Response                           NOT:   Section 9.2

Stewart_Essential Calc_2ET ch10sec02

MULTIPLE CHOICE

1. Find .

 a. b. , c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    10.2.13

MSC:   Bimodal          NOT:   Section 10.2

1. Find .

 a. b. c. 27 d. 90 e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    10.2.15

MSC:   Bimodal          NOT:   Section 10.2

1. Find the unit vectors that are parallel to the tangent line to the curve  at the point .

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    10.2.33

MSC:   Bimodal          NOT:   Section 10.2

NUMERIC RESPONSE

1. A woman walks due west on the deck of a ship at  mi/h. The ship is moving north at a speed of   mi/h. Find the speed of the woman relative to the surface of the water. Round the result to the nearest tenth.

ANS:

PTS:    1                      DIF:    Medium          REF:    10.2.27

MSC:   Numerical Response                           NOT:   Section 10.2

1. The tension T at each end of the chain has magnitude  N and makes an angle  with the horizontal. What is the weight of the chain? Round the result to the nearest hundredth.

ANS:

PTS:    1                      DIF:    Medium          REF:    10.2.30

MSC:   Numerical Response                           NOT:   Section 10.2

Stewart_Essential Calc_2ET ch11sec02

MULTIPLE CHOICE

1. Find the limit

 a. 34 b. 260 c. 80 d. 16

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    11.2.3

MSC:   Bimodal          NOT:   Section 11.2

1. Evaluate the limit.

 a. b. 0 c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    11.2.9

MSC:   Bimodal          NOT:   Section 11.2

1. Find the limit

 a. b. c. d.

ANS:   A                     PTS:    1                      DIF:    Easy                REF:    11.2.11

MSC:   Bimodal          NOT:   Section 11.2

1. Evaluate the limit.

 a. 0 b. the limit does not exist c. d. 1 e. 2

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    11.2.12

MSC:   Bimodal          NOT:   Section 11.2

1. Find the limit

 a. b. c. d.

ANS:   B                     PTS:    1                      DIF:    Easy                REF:    11.2.15

MSC:   Bimodal          NOT:   Section 11.2

1. Find the limit

 a. b. c. d.

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    11.2.16

MSC:   Bimodal          NOT:   Section 11.2

1. Determine the largest set on which the function is continuous.

 a. b. c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    11.2.25

MSC:   Bimodal          NOT:   Section 11.2

1. Determine where the function  is continuous.

 a. b. c. d.

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    11.2.28

MSC:   Bimodal          NOT:   Section 11.2

NUMERIC RESPONSE

1. Find the limit.

ANS:

PTS:    1                      DIF:    Medium          REF:    11.2.4

MSC:   Numerical Response                           NOT:   Section 11.2

1. Find , if   and .

ANS:

PTS:    1                      DIF:    Medium          REF:    11.2.19

MSC:   Numerical Response                           NOT:   Section 11.2

1. Determine the largest set on which the function is continuous.

ANS:

PTS:    1                      DIF:    Medium          REF:    11.2.27

MSC:   Numerical Response                           NOT:   Section 11.2

1. Use spherical coordinates to find the limit.

ANS:   0

PTS:    1                      DIF:    Medium          REF:    11.2.29

MSC:   Numerical Response                           NOT:   Section 11.2

1. Determine where the function  is continuous.

ANS:

PTS:    1                      DIF:    Medium          REF:    11.2.21            MSC:   Short Answer

NOT:   Section 11.2

Stewart_Essential Calc_2ET ch12sec02

MULTIPLE CHOICE

1. Find the volume under  and above the region bounded by  and  .

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    12.2.22

MSC:   Bimodal          NOT:   Section 12.2

NUMERIC RESPONSE

1. Calculate the iterated integral.

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.5

MSC:   Numerical Response                           NOT:   Section 12.2

1. Evaluate the double integral.

is bounded by  and .

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.15

MSC:   Numerical Response                           NOT:   Section 12.2

1. Evaluate the double integral.

,  is triangular region with vertices .

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.17

MSC:   Numerical Response                           NOT:   Section 12.2

1. Evaluate the double integral.

is bounded by the circle with center the origin and radius .

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.19

MSC:   Numerical Response                           NOT:   Section 12.2

1. Evaluate  where  is the figure bounded by  and  .

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.20

MSC:   Numerical Response                           NOT:   Section 12.2

1. Evaluate the integral by reversing the order of integration.

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.43

MSC:   Numerical Response                           NOT:   Section 12.2

1. Evaluate the integral by reversing the order of integration.

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.47

MSC:   Numerical Response                           NOT:   Section 12.2

1. Evaluate the double integral , where  is the region bounded by the graphs of  and .

ANS:

PTS:    1                      DIF:    Medium          REF:    12.2.12            MSC:   Short Answer

NOT:   Section 12.2

1. Evaluate the iterated integral  by reversing the order of integration.

ANS:

PTS:    1                      DIF:    Difficult          REF:    12.2.44            MSC:   Short Answer

NOT:   Section 12.2

Stewart_Essential Calc_2ET ch13sec02

MULTIPLE CHOICE

1. Evaluate  where C is the right half of the circle

 a. b. c. d. e.

ANS:   A                     PTS:    1                      DIF:    Medium          REF:    13.2.3

MSC:   Bimodal          NOT:   Section 13.2

1. Evaluate the line integral over the given curve C.

; ,

 a. b. c. d.

ANS:   D                     PTS:    1                      DIF:    Medium          REF:    13.2.28

MSC:   Bimodal          NOT:   Section 13.2

1. A thin wire is bent into the shape of a semicircle  If the linear density is , find the exact mass of the wire.

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    13.2.31

MSC:   Bimodal          NOT:   Section 13.2

1. Find the exact mass of a thin wire in the shape of the helix  if the density is 5.

 a. b. c. d. e.

ANS:   D                     PTS:    1                      DIF:    Medium          REF:    13.2.34

MSC:   Bimodal          NOT:   Section 13.2

1. Find the work done by the force field  on a particle that moves along the parabola

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    13.2.38

MSC:   Bimodal          NOT:   Section 13.2

NUMERIC RESPONSE

1. Find the work done by the force field  in moving an object along an arch of the cycloid

ANS:

PTS:    1                      DIF:    Medium          REF:    13.2.37

MSC:   Numerical Response                           NOT:   Section 13.2

1. Evaluate the line integral over the given curve C.

, where C is the line segment joining (–2, –1) to (4, 5)

ANS:

PTS:    1                      DIF:    Medium          REF:    13.2.10            MSC:   Short Answer

NOT:   Section 13.2

Stewart_Essential Calc_2ET ch13sec07

MULTIPLE CHOICE

1. Suppose that   where g is a function of one variable such that  .

Evaluate   where S is the sphere

1. None of these

ANS:      A             PTS:       1              DIF:        Medium               REF:       13.7.4

MSC:     Bimodal                NOT:      Section 13.7

1. Evaluate the surface integral.

S is the part of the plane   that lies in the first octant.

ANS:      A             PTS:       1              DIF:        Medium               REF:       13.7.10

MSC:     Bimodal                NOT:      Section 13.7

1. Evaluate the surface integral. Round your answer to four decimal places.

S is surface

ANS:      D             PTS:       1              DIF:        Medium               REF:       13.7.14

MSC:     Bimodal                NOT:      Section 13.7

1. The temperature at the point   in a substance with conductivity   is

Find the rate of heat flow inward across the cylindrical

ANS:      C             PTS:       1              DIF:        Medium               REF:       13.7.45

MSC:     Bimodal                NOT:      Section 13.7

NUMERIC RESPONSE

1. Evaluate the surface integral    for the given vector field F and the oriented surface S. In other words, find the flux of F across S.

in the first octant, with orientation toward the origin.

ANS:

PTS:       1              DIF:        Medium               REF:       13.7.25

MSC:     Numerical Response                      NOT:      Section 13.7

1. Evaluate the surface integral   for the given vector field F and the oriented surface S. In other words, find the flux of F across S.

ANS:      144

PTS:       1              DIF:        Medium               REF:       13.7.29

MSC:     Numerical Response                      NOT:      Section 13.7

1. Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone   if its density function is

ANS:

PTS:       1              DIF:        Medium               REF:       13.7.39b

MSC:     Numerical Response                      NOT:      Section 13.7

1. A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid

ANS:

PTS:       1              DIF:        Medium               REF:       13.7.41

MSC:     Numerical Response                      NOT:      Section 13.7

1. Use Gauss’s Law to find the charge contained in the solid hemisphere  ,  if the electric field is

ANS:

PTS:       1              DIF:        Medium               REF:       13.7.43

MSC:     Numerical Response                      NOT:      Section 13.7

Stewart_Essential Calc_2ET ch03sec01

MULTIPLE CHOICE

1. Starting with the graph of , write the equation of the graph that results from shifting 5 units right.

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    3.1.13b

MSC:   Bimodal          NOT:   Section 3.1

1. Starting with the graph of , find the equation of the graph that results from reflecting about the line .

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    3.1.14a

MSC:   Bimodal          NOT:   Section 3.1

1. Find the exponential function  whose graph is given.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    3.1.18

MSC:   Bimodal          NOT:   Section 3.1

1. Find the limit.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Easy                REF:    3.1.24

MSC:   Bimodal          NOT:   Section 3.1

1. Find the limit.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Easy                REF:    3.1.25

MSC:   Bimodal          NOT:   Section 3.1

Stewart_Essential Calc_2ET ch03sec03

MULTIPLE CHOICE

1. Differentiate the function.

 a. b. c. d.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    3.3.14

MSC:   Bimodal          NOT:   Section 3.3

1. Use logarithmic differentiation to find the derivative of the function.

 a. b. c. d.

ANS:   C                     PTS:    1                      DIF:    Difficult          REF:    3.3.53

MSC:   Bimodal          NOT:   Section 3.3

1. Use logarithmic differentiation to find the derivative of the function.

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Medium          REF:    3.3.55

MSC:   Bimodal          NOT:   Section 3.3

1. If , find .

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    3.3.69

MSC:   Bimodal          NOT:   Section 3.3

1. Find .

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    3.3.72

MSC:   Bimodal          NOT:   Section 3.3

NUMERIC RESPONSE

1. Differentiate the function.

ANS:

PTS:    1                      DIF:    Medium          REF:    3.3.18

MSC:   Numerical Response                           NOT:   Section 3.3

1. Differentiate the function.

ANS:

PTS:    1                      DIF:    Medium          REF:    3.3.35              MSC:   Short Answer

NOT:   Section 3.3

1. Find an equation of the tangent line to the curve

at .

ANS:

PTS:    1                      DIF:    Difficult          REF:    3.3.45              MSC:   Short Answer

NOT:   Section 3.3

Stewart_Essential Calc_2ET ch03sec04

MULTIPLE CHOICE

1. Strontium- has a half-life of  days. A sample has a mass of  mg initially. Find a formula for the mass remaining after  days.

 a. b. c. d. e.

ANS:  A                    PTS:   1                    DIF:    Easy               REF:   3.4.8a

MSC:  Bimodal         NOT:  Section 3.4

1. The half-life of cesium  is  years. Suppose we have a -mg sample. Find the mass that remains after  years.

 a. b. c. d. e.

ANS:  A                    PTS:   1                    DIF:    Easy               REF:   3.4.9a

MSC:  Bimodal         NOT:  Section 3.4

1. The half-life of cesium- is  years. Suppose we have a -mg sample. How much of the sample remains after  years?

 a. b. c. d. e.

ANS:  D                    PTS:   1                    DIF:    Easy               REF:   3.4.9b

MSC:  Bimodal         NOT:  Section 3.4

1. If  is invested at  interest, find the value of the investment at the end of  years if the interest is compounded .

 a. b. c. d. e.

ANS:  E                    PTS:   1                    DIF:    Easy               REF:   3.4.18a

MSC:  Bimodal         NOT:  Section 3.4

1. If  is invested at  interest, find the value of the investment at the end of  years if the interest is compounded .

 a. b. c. d. e.

ANS:  C                    PTS:   1                    DIF:    Easy               REF:   3.4.19

MSC:  Bimodal         NOT:  Section 3.4

Stewart_Essential Calc_2ET ch03sec05

MULTIPLE CHOICE

1. Find the exact value of the expression.

 a. b. c. d. e.

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    3.5.2b

MSC:   Bimodal          NOT:   Section 3.5

1. Find the exact value of the expression.

 a. b. c. d. e.

ANS:   A                     PTS:    1                      DIF:    Easy                REF:    3.5.3a

MSC:   Bimodal          NOT:   Section 3.5

1. Simplify the expression.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Easy                REF:    3.5.9

MSC:   Bimodal          NOT:   Section 3.5

1.  ________

 a. b. c. d. e.

ANS:   C                     PTS:    1                      DIF:    Easy                REF:    3.5.13

MSC:   Bimodal          NOT:   Section 3.5

1. Find the derivative of the function. Simplify where possible.

 a. b. c. d. e.

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    3.5.16

MSC:   Bimodal          NOT:   Section 3.5

Stewart_Essential Calc_2ET ch03sec06

MULTIPLE CHOICE

1. Find the numerical value of the expression.

 a. b. c. d. e.

ANS:   E                     PTS:    1                      DIF:    Easy                REF:    3.6.1a

MSC:   Bimodal          NOT:   Section 3.6

1. Find the value of the expression accurate to four decimal places.

sinh 4

 a. 29.3082 c. 15.145 b. 55.5798 d. 27.2899

ANS:   D                     PTS:    1                      DIF:    Easy                REF:    3.6.3b

MSC:   Bimodal          NOT:   Section 3.6

1. Find the numerical value of the expression.

 a. b. c. d. e.

ANS:   B                     PTS:    1                      DIF:    Easy                REF:    3.6.6a

MSC:   Bimodal          NOT:   Section 3.6

1. Find the derivative.

 a. b. c. d. e.

ANS:   D                     PTS:    1                      DIF:    Medium          REF:    3.6.29

MSC:   Bimodal          NOT:   Section 3.6

1. A telephone line hangs between two poles at 12 m apart in the shape of the catenary

,

where x and y are measured in meters. Find the slope of this curve where it meets the right pole.

 a. b. c. d. e.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    3.6.47a

MSC:   Bimodal          NOT:   Section 3.6

Stewart_Essential Calc_2ET ch03sec07

MULTIPLE CHOICE

1. Evaluate the limit using l’Hôpital’s Rule.

 a. 75 b. 25 c. 15 d.

ANS:   A                     PTS:    1                      DIF:    Easy                REF:    3.7.9

MSC:   Bimodal          NOT:   Section 3.7

1. Evaluate the limit using l’Hôpital’s Rule.

 a. b. 3 c. 0 d.

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    3.7.12

MSC:   Bimodal          NOT:   Section 3.7

1. Find the limit.

 a. b. 0 c. d. 1 e.

ANS:   E                     PTS:    1                      DIF:    Medium          REF:    3.7.29

MSC:   Bimodal          NOT:   Section 3.7

1. Evaluate the limit using l’Hôpital’s Rule.

 a. 0 b. 1 c. ¥ d. e

ANS:   C                     PTS:    1                      DIF:    Medium          REF:    4.4.25

MSC:   Bimodal          NOT:   Section 4.4

NUMERIC RESPONSE

1. Find the limit.

ANS:

PTS:    1                      DIF:    Medium          REF:    3.7.18

MSC:   Numerical Response                           NOT:   Section 3.7