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  1. Preface
  2. 1 Functions and Graphs
    1. Introduction
    2. 1.1 Review of Functions
    3. 1.2 Basic Classes of Functions
    4. 1.3 Trigonometric Functions
    5. 1.4 Inverse Functions
    6. 1.5 Exponential and Logarithmic Functions
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Chapter Review Exercises
  3. 2 Limits
    1. Introduction
    2. 2.1 A Preview of Calculus
    3. 2.2 The Limit of a Function
    4. 2.3 The Limit Laws
    5. 2.4 Continuity
    6. 2.5 The Precise Definition of a Limit
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Chapter Review Exercises
  4. 3 Derivatives
    1. Introduction
    2. 3.1 Defining the Derivative
    3. 3.2 The Derivative as a Function
    4. 3.3 Differentiation Rules
    5. 3.4 Derivatives as Rates of Change
    6. 3.5 Derivatives of Trigonometric Functions
    7. 3.6 The Chain Rule
    8. 3.7 Derivatives of Inverse Functions
    9. 3.8 Implicit Differentiation
    10. 3.9 Derivatives of Exponential and Logarithmic Functions
    11. Key Terms
    12. Key Equations
    13. Key Concepts
    14. Chapter Review Exercises
  5. 4 Applications of Derivatives
    1. Introduction
    2. 4.1 Related Rates
    3. 4.2 Linear Approximations and Differentials
    4. 4.3 Maxima and Minima
    5. 4.4 The Mean Value Theorem
    6. 4.5 Derivatives and the Shape of a Graph
    7. 4.6 Limits at Infinity and Asymptotes
    8. 4.7 Applied Optimization Problems
    9. 4.8 L’Hôpital’s Rule
    10. 4.9 Newton’s Method
    11. 4.10 Antiderivatives
    12. Key Terms
    13. Key Equations
    14. Key Concepts
    15. Chapter Review Exercises
  6. 5 Integration
    1. Introduction
    2. 5.1 Approximating Areas
    3. 5.2 The Definite Integral
    4. 5.3 The Fundamental Theorem of Calculus
    5. 5.4 Integration Formulas and the Net Change Theorem
    6. 5.5 Substitution
    7. 5.6 Integrals Involving Exponential and Logarithmic Functions
    8. 5.7 Integrals Resulting in Inverse Trigonometric Functions
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Chapter Review Exercises
  7. 6 Applications of Integration
    1. Introduction
    2. 6.1 Areas between Curves
    3. 6.2 Determining Volumes by Slicing
    4. 6.3 Volumes of Revolution: Cylindrical Shells
    5. 6.4 Arc Length of a Curve and Surface Area
    6. 6.5 Physical Applications
    7. 6.6 Moments and Centers of Mass
    8. 6.7 Integrals, Exponential Functions, and Logarithms
    9. 6.8 Exponential Growth and Decay
    10. 6.9 Calculus of the Hyperbolic Functions
    11. Key Terms
    12. Key Equations
    13. Key Concepts
    14. Chapter Review Exercises
  8. A | Table of Integrals
  9. B | Table of Derivatives
  10. C | Review of Pre-Calculus
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
  12. Index

Checkpoint

1.1

f(1)=3f(1)=3 and f(a+h)=a2+2ah+h23a3h+5f(a+h)=a2+2ah+h23a3h+5

1.2

Domain = {x|x2},{x|x2}, range = {y|y5}{y|y5}

1.3

x=0,2,3x=0,2,3

1.4

(fg)(x)=x2+32x5.(fg)(x)=x2+32x5. The domain is {x|x52}.{x|x52}.

1.5

(fg)(x)=25x.(fg)(x)=25x.

1.6

(gf)(x)=0.63x(gf)(x)=0.63x

1.7

f(x)f(x) is odd.

1.8

Domain = (,),(,), range = {y|y−4}.{y|y−4}.

1.9

m=1/2.m=1/2. The point-slope form is

y4=12(x1).y4=12(x1).

The slope-intercept form is

y=12x+72.y=12x+72.

1.10

The zeros are x=1±3/3.x=1±3/3. The parabola opens upward.

1.11

The domain is the set of real numbers xx such that x1/2.x1/2. The range is the set {y|y5/2}.{y|y5/2}.

1.12

The domain of ff is (−∞, ∞).(−∞, ∞). The domain of gg is {x|x1/5}.{x|x1/5}.

1.13

Algebraic

1.15

C(x)={49,0<x170,1<x291,2<x3C(x)={49,0<x170,1<x291,2<x3

1.16

Shift the graph y=x2y=x2 to the left 1 unit, reflect about the xx-axis, then shift down 4 units.

1.17

7π/6;7π/6; 330°

1.18

cos(3π/4)=2/2;sin(π/6)=−1/2cos(3π/4)=2/2;sin(π/6)=−1/2

1.19

1010 ft

1.20

θ=3π2+2nπ,π6+2nπ,5π6+2nπθ=3π2+2nπ,π6+2nπ,5π6+2nπ for n=0,±1,±2,…n=0,±1,±2,…

1.22

To graph f(x)=3sin(4x)5,f(x)=3sin(4x)5, the graph of y=sin(x)y=sin(x) needs to be compressed horizontally by a factor of 4, then stretched vertically by a factor of 3, then shifted down 5 units. The function ff will have a period of π/2π/2 and an amplitude of 3.

1.23

No.

1.24

f−1(x)=2xx3.f−1(x)=2xx3. The domain of f−1f−1 is {x|x3}.{x|x3}. The range of f−1f−1 is {y|y2}.{y|y2}.

1.26

The domain of f−1f−1 is (0,).(0,). The range of f−1f−1 is (,0).(,0). The inverse function is given by the formula f−1(x)=−1/x.f−1(x)=−1/x.

1.27

f(4)=900;f(10)=24,300.f(4)=900;f(10)=24,300.

1.28

x/(2y3)x/(2y3)

1.29

A(t)=750e0.04t.A(t)=750e0.04t. After 3030 years, there will be approximately $2,490.09.$2,490.09.

1.30

x=ln32x=ln32

1.31

x=1ex=1e

1.32

1.292481.29248

1.33

The magnitude 8.48.4 earthquake is roughly 1010 times as severe as the magnitude 7.47.4 earthquake.

1.34

(x2+x−2)/2(x2+x−2)/2

1.35

12ln(3)0.5493.12ln(3)0.5493.

Section 1.1 Exercises

1.

a. Domain = {−3,−2,−1,0,1,2,3},{−3,−2,−1,0,1,2,3}, range = {0,1,4,9}{0,1,4,9} b. Yes, a function

3.

a. Domain = {0,1,2,3},{0,1,2,3}, range = {−3,−2,−1,0,1,2,3}{−3,−2,−1,0,1,2,3} b. No, not a function

5.

a. Domain = {3,5,8,10,15,21,33},{3,5,8,10,15,21,33}, range = {0,1,2,3}{0,1,2,3} b. Yes, a function

7.

a. −2−2 b. 3 c. 13 d. −5x2−5x2 e. 5a25a2 f. 5a+5h25a+5h2

9.

a. Undefined b. 2 c. 2323 d. 2x2x e 2a2a f. 2a+h2a+h

11.

a. 55 b. 1111 c. 2323 d. −6x+5−6x+5 e. 6a+56a+5 f. 6a+6h+56a+6h+5

13.

a. 9 b. 9 c. 9 d. 9 e. 9 f. 9

15.

x18;y0;x=18;x18;y0;x=18; no y-intercept

17.

x−2;y−1;x=−1;y=−1+2x−2;y−1;x=−1;y=−1+2

19.

x4;y0;x4;y0; no x-intercept; y=34y=34

21.

x>5;y>0;x>5;y>0; no intercepts

23.


An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -3 to 3. The graph is of the function “f(x) = 3x - 6”, which is an increasing straight line. The function has an x intercept at (2, 0) and the y intercept is not shown.
25.


An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -2 to 6. The graph is of the function “f(x) = 2 times the absolute value of x”. The function decreases in a straight line until it hits the origin, then begins to increase in a straight line. The function x intercept and y intercept are at the origin.
27.


An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -27 to 27. The graph is of the function “f(x) = x cubed”. The curved function increases until it hits the origin, where it levels out and then becomes even. After the origin the graph begins to increase again. The x intercept and y intercept are both at the origin.
29.

Function; a. Domain: all real numbers, range: y0y0 b. x=±1x=±1 c. y=1y=1 d. −1<x<0−1<x<0 and 1<x<1<x< e. <x<1<x<1 and 0<x<10<x<1 f. Not constant g. y-axis h. Even

31.

Function; a. Domain: all real numbers, range: −1.5y1.5−1.5y1.5 b. x=0x=0 c. y=0y=0 d. all real numbersall real numbers e. None f. Not constant g. Origin h. Odd

33.

Function; a. Domain: <x<,<x<, range: −2y2−2y2 b. x=0x=0 c. y=0y=0 d. −2<x<2−2<x<2 e. Not decreasing f. <x<2<x<2 and 2<x<2<x< g. Origin h. Odd

35.

Function; a. Domain: −4x4,−4x4, range: −4y4−4y4 b. x=1.2x=1.2 c. y=4y=4 d. Not increasing e. 0<x<40<x<4 f. −4<x<0−4<x<0 g. No Symmetry h. Neither

37.

a. 5x2+x8;5x2+x8; all real numbers b. −5x2+x8;−5x2+x8; all real numbers c. 5x340x2;5x340x2; all real numbers d. x85x2;x0x85x2;x0

39.

a. −2x+6;−2x+6; all real numbers b. −2x2+2x+12;−2x2+2x+12; all real numbers c. x4+2x3+12x218x27;x4+2x3+12x218x27; all real numbers d. x+3x+1;x1,3x+3x+1;x1,3

41.

a. 6+2x;x06+2x;x0 b. 6; x0x0 c. 6x+1x2;x06x+1x2;x0 d. 6x+1;x06x+1;x0

43.

a. 4x+3;4x+3; all real numbers b. 4x+15;4x+15; all real numbers

45.

a. x46x2+16;x46x2+16; all real numbers b. x4+14x2+46;x4+14x2+46; all real numbers

47.

a. 3x4+x;x0,−43x4+x;x0,−4 b. 4x+23;x124x+23;x12

49.

a. Yes, because there is only one winner for each year. b. No, because there are three teams that won more than once during the years 2001 to 2012.

51.

a. V(s)=s3V(s)=s3 b. V(11.8)1643;V(11.8)1643; a cube of side length 11.8 each has a volume of approximately 1643 cubic units.

53.

a. N(x)=15xN(x)=15x b. i. N(20)=15(20)=300;N(20)=15(20)=300; therefore, the vehicle can travel 300 mi on a full tank of gas. Ii. N(15)=225;N(15)=225; therefore, the vehicle can travel 225 mi on 3/4 of a tank of gas. c. Domain: 0x20;0x20; range: [0,300][0,300] d. The driver had to stop at least once, given that it takes approximately 39 gal of gas to drive a total of 578 mi.

55.

a. A(t)=A(r(t))=π·(65t2+1)2A(t)=A(r(t))=π·(65t2+1)2 b. Exact: 121π4;121π4; approximately 95 cm2 c. C(t)=C(r(t))=2π(65t2+1)C(t)=C(r(t))=2π(65t2+1) d. Exact: 11π;11π; approximately 35 cm

57.

a. S(x)=8.5x+750S(x)=8.5x+750 b. $962.50, $1090, $1217.50 c. 77 skateboards

Section 1.2 Exercises

59.

a. −1 b. Decreasing

61.

a. 3/4 b. Increasing

63.

a. 4/3 b. Increasing

65.

a. 0 b. Horizontal

67.

y=−6x+9y=−6x+9

69.

y=13x+4y=13x+4

71.

y=12xy=12x

73.

y=35x3y=35x3

75.

a. (m=2,b=−3)(m=2,b=−3) b.

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows an increasing straight line function with a y intercept at (0, -3) and a x intercept at (1.5, 0).
77.

a. (m=−6,b=0)(m=−6,b=0) b.

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a decreasing straight line function with a y intercept and x intercept both at the origin. There is an unlabeled point on the function at (0.5, -3).
79.

a. (m=0,b=−6)(m=0,b=−6) b.

An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -7 to 1. The graph shows a horizontal straight line function with a y intercept at (0, -6) and no x intercept.
81.

a. (m=23,b=2)(m=23,b=2) b.

An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -4 to 4. The graph shows a decreasing straight line function with a y intercept at (0, 2) and a x intercept at (3, 0).
83.

a. 2 b. 52,−1;52,−1; c. −5 d. Both ends rise e. Neither

85.

a. 2 b. ±2±2 c. −1 d. Both ends rise e. Even

87.

a. 3 b. 0, ±3±3 c. 0 d. Left end rises, right end falls e. Odd

89.


An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a parabolic function that decreases until the point (-3, 1), then begins increasing. The y intercept is not shown and there are no x intercepts. There are two unplotted points at (-4, 2) and (-2, 2).
91.


An image of a graph. The x axis runs from -5 to 20 and the y axis runs from -8 to 2. The graph shows a curved function that begins at the point (0, -1), then begins decreasing. The y intercept is at (0, -1) and there is no x intercept. There is an unplotted point at (9, -4).
93.


An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a function that starts at point (-2, 2), where it begins to increase until the point (0, 4). After the point (0, 4), the function becomes a horizontal line and stays that way until the point (2, 4). After the point (2, 4), the function begins to decrease until the point (4, 2), where the function ends.
95.

a. 13,−3,513,−3,5 b.

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a function that has two pieces. The first piece is a decreasing curve that ends at the point (0, -3). The second piece is an increasing line that begins at the point (0, -3). The function has a x intercepts at the approximate point (1.7, 0) and the point (0.75, 0) and a y intercept at (0, -3).
97.

a. −32,−12,4−32,−12,4 b.

An image of a graph. The x axis runs from -10 to 10 and the y axis runs from -10 to 10. The graph is of a function that begins slightly below the x axis and begins to decrease. As the function approaches the unplotted vertical line of “x = 2”, it decreases at a faster rate but never reaches the line “x = 2”. On the right side of the unplotted line “x = 2”, the function starts at the top of graph and begins decreasing and approaches the unplotted horizontal line “y = 0”, but never reaches “y = 0”. There function also includes a plotted point at (2, 4). There is a y intercept at (0, -1.5) and no x intercept.
99.

True; n=3n=3

101.

False; f(x)=xb,f(x)=xb, where bb is a real-valued constant, is a power function

103.

a. V(t)=−2733t+20500V(t)=−2733t+20500 b. (0,20,500)(0,20,500) means that the initial purchase price of the equipment is $20,500; (7.5,0)(7.5,0) means that in 7.5 years the computer equipment has no value. c. $6835 d. In approximately 6.4 years

105.

a. C=0.75x+125C=0.75x+125 b. $245 c. 167 cupcakes

107.

a. V(t)=−1500t+26,000V(t)=−1500t+26,000 b. In 4 years, the value of the car is $20,000.

109.

$30,337.50

111.

96% of the total capacity

Section 1.3 Exercises

113.

4π3rad4π3rad

115.

π3π3

117.

11π6rad11π6rad

119.

210°210°

121.

−540°−540°

123.

−0.5−0.5

125.

2222

127.

31223122

129.

a. b=5.7b=5.7 b. sinA=47,cosA=5.77,tanA=45.7,cscA=74,secA=75.7,cotA=5.74sinA=47,cosA=5.77,tanA=45.7,cscA=74,secA=75.7,cotA=5.74

131.

a. c=151.7c=151.7 b. sinA=0.5623,cosA=0.8273,tanA=0.6797,cscA=1.778,secA=1.209,cotA=1.471sinA=0.5623,cosA=0.8273,tanA=0.6797,cscA=1.778,secA=1.209,cotA=1.471

133.

a. c=85c=85 b. sinA=8485,cosA=1385,tanA=8413,cscA=8584,secA=8513,cotA=1384sinA=8485,cosA=1385,tanA=8413,cscA=8584,secA=8513,cotA=1384

135.

a. y=2425y=2425 b. sinθ=2425,cosθ=725,tanθ=247,cscθ=2524,secθ=257,cotθ=724sinθ=2425,cosθ=725,tanθ=247,cscθ=2524,secθ=257,cotθ=724

137.

a. x=23x=23 b. sinθ=73,cosθ=23,tanθ=142,cscθ=377,secθ=−322,cotθ=147sinθ=73,cosθ=23,tanθ=142,cscθ=377,secθ=−322,cotθ=147

139.

sec2xsec2x

141.

sin2xsin2x

143.

sec2θsec2θ

145.

1sint=csct1sint=csct

155.

{π6,5π6}{π6,5π6}

157.

{π4,3π4,5π4,7π4}{π4,3π4,5π4,7π4}

159.

{2π3,5π3}{2π3,5π3}

161.

{0,π,π3,5π3}{0,π,π3,5π3}

163.

y=4sin(π4x)y=4sin(π4x)

165.

y=cos(2πx)y=cos(2πx)

167.

a. 1 b. 2π2π c. π4π4 units to the right

169.

a. 1212 b. 8π8π c. No phase shift

171.

a. 3 b. 22 c. 2π2π units to the left

173.

Approximately 42 in.

175.

a. 0.550 rad/sec b. 0.236 rad/sec c. 0.698 rad/min d. 1.697 rad/min

177.

30.9in230.9in2

179.

a. π/184; the voltage repeats every π/184 sec b. Approximately 59 periods

181.

a. Amplitude = 10;period=2410;period=24 b. 47.4°F47.4°F c. 14 hours later, or 2 p.m. d.

An image of a graph. The x axis runs from 0 to 365 and is labeled “t, hours after midnight”. The y axis runs from 0 to 20 and is labeled “T, degrees in Fahrenheit”. The graph is of a curved wave function that starts at the approximate point (0, 41.3) and begins decreasing until the point (2, 40). After this point, the function increases until the point (14, 60). After this point, the function begins decreasing again.

Section 1.4 Exercises

183.

Not one-to-one

185.

Not one-to-one

187.

One-to-one

189.

a. f−1(x)=x+4f−1(x)=x+4 b. Domain :x−4,range:y0:x−4,range:y0

191.

a. f−1(x)=x13f−1(x)=x13 b. Domain: all real numbers, range: all real numbers

193.

a. f−1(x)=x2+1,f−1(x)=x2+1, b. Domain: x0,x0, range: y1y1

195.


An image of a graph. The x axis runs from -4 to 4 and the y axis runs from -4 to 4. The graph is of two functions. The first function is an increasing straight line function labeled “f”. The x intercept is at (-2, 0) and y intercept are both at (0, 1). The second function is of an increasing straight line function labeled “f inverse”. The x intercept is at the point (1, 0) and the y intercept is at the point (0, -2).
197.


An image of a graph. The x axis runs from 0 to 8 and the y axis runs from 0 to 8. The graph is of two function. The first function is an increasing straight line function labeled “f”. The function starts at the point (0, 1) and increases in straight line until the point (4, 6). After this point, the function continues to increase, but at a slower rate than before, as it approaches the point (8, 8). The function does not have an x intercept and the y intercept is (0, 1). The second function is an increasing straight line function labeled “f inverse”. The function starts at the point (1, 0) and increases in straight line until the point (6, 4). After this point, the function continues to increase, but at a faster rate than before, as it approaches the point (8, 8). The function does not have an y intercept and the x intercept is (1, 0).
199.

These are inverses.

201.

These are not inverses.

203.

These are inverses.

205.

These are inverses.

207.

π6π6

209.

π4π4

211.

π6π6

213.

2222

215.

π6π6

217.

a. x=f−1(V)=0.04V500x=f−1(V)=0.04V500 b. The inverse function determines the distance from the center of the artery at which blood is flowing with velocity V. c. 0.1 cm; 0.14 cm; 0.17 cm

219.

a. $31,250, $66,667, $107,143 b. (p=85CC+75)(p=85CC+75) c. 34 ppb

221.

a. ~92°~92° b. ~42°~42° c. ~27°~27°

223.

x6.69,8.51;x6.69,8.51; so, the temperature occurs on June 21 and August 15

225.

~1.5sec~1.5sec

227.

tan−1(tan(2.1))1.0416;tan−1(tan(2.1))1.0416; the expression does not equal 2.1 since 2.1>1.57=π22.1>1.57=π2—in other words, it is not in the restricted domain of tanx.cos−1(cos(2.1))=2.1,tanx.cos−1(cos(2.1))=2.1, since 2.1 is in the restricted domain of cosx.cosx.

Section 1.5 Exercises

229.

a. 125 b. 2.24 c. 9.74

231.

a. 0.01 b. 10,000 c. 46.42

233.

d

235.

b

237.

e

239.

Domain: all real numbers, range: (2,),y=2(2,),y=2

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved increasing function that starts slightly above the line “y = 2” and begins increasing rapidly. There is no x intercept and the y intercept is at the point (0, 3).
241.

Domain: all real numbers, range: (0,),y=0(0,),y=0

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved increasing function that starts slightly above the x axis and begins increasing rapidly. There is no x intercept and the y intercept is at the point (0, 3). Another point of the graph is at (-1, 1).
243.

Domain: all real numbers, range: (,1),y=1(,1),y=1

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved increasing function that increases until it comes close the line “y = 1” without touching it. There x intercept and the y intercept are both at the origin. Another point of the graph is at (-1, -1).
245.

Domain: all real numbers, range: (−1,),y=−1(−1,),y=−1

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved decreasing function that decreases until it comes close the line “y = -1” without touching it. There x intercept and the y intercept are both at the origin. There is an approximate point on the graph at (-1, 1.7).
247.

81/3=281/3=2

249.

52=2552=25

251.

e−3=1e3e−3=1e3

253.

e0=1e0=1

255.

log4(116)=−2log4(116)=−2

257.

log91=0log91=0

259.

log644=13log644=13

261.

log9150=ylog9150=y

263.

log40.125=32log40.125=32

265.

Domain: (1,),(1,), range: (,),x=1(,),x=1

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of an increasing curved function which starts slightly to the right of the vertical line “x = 1”. There is no y intercept and the x intercept is at the approximate point (2, 0).
267.

Domain: (0,),(0,), range: (,),x=0(,),x=0

An image of a graph. The x axis runs from -1 to 9 and the y axis runs from -5 to 5. The graph is of a decreasing curved function which starts slightly to the right of the y axis. There is no y intercept and the x intercept is at the point (e, 0).
269.

Domain: (−1,),(−1,), range: (,),x=−1(,),x=−1

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of an increasing curved function which starts slightly to the right of the vertical line “x = -1”. There y intercept and the x intercept are both at the origin.
271.

2+3log3alog3b2+3log3alog3b

273.

32+12log5x+32log5y32+12log5x+32log5y

275.

32+ln632+ln6

277.

ln153ln153

279.

3232

281.

log7.21log7.21

283.

23+log113log723+log113log7

285.

x=125x=125

287.

x=4x=4

289.

x=3x=3

291.

1+51+5

293.

(log82log72.2646)(log82log72.2646)

295.

(log211log0.57.7211)(log211log0.57.7211)

297.

(log0.452log0.20.4934)(log0.452log0.20.4934)

299.

~17,491~17,491

301.

Approximately $131,653 is accumulated in 5 years.

303.

i. a. pH = 8 b. Base ii. a. pH = 3 b. Acid iii. a. pH = 4 b. Acid

305.

a. ~333~333 million b. 94 years from 2013, or in 2107

307.

a. k0.0578k0.0578 b. 9292 hours

309.

The San Francisco earthquake had 103.4or~2512103.4or~2512 times more energy than the Japan earthquake.

Chapter Review Exercises

311.

False

313.

False

315.

Domain: x>5,x>5, range: all real numbers

317.

Domain: x>2x>2 and x<4,x<4, range: all real numbers

319.

Degree of 3, yy-intercept: 0, zeros: 0, 31,−1331,−13

321.

cos2xsin2x=cos2xcos2xsin2x=cos2x or = 12sin2x 2 = 12sin2x 2 or = 2cos2x1 2 = 2cos2x1 2

323.

0,±2π0,±2π

325.

4

327.

One-to-one; yes, the function has an inverse; inverse: f−1(x)=1yf−1(x)=1y

329.

x32,f−1(x)=32+124y7x32,f−1(x)=32+124y7

331.

a. C(x)=300+7xC(x)=300+7x b. 100 shirts

333.

The population is less than 20,000 from December 8 through January 23 and more than 140,000 from May 29 through August 2

335.

78.51%

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