Calculus of A Single Variable 7th Edition solutions | StudySoup

Calculus

Calculus of A Single Variable | 7th Edition | ISBN: 9780618149162 | Authors: Ron Larson, Robert P. Hostetler, Bruce H. Edwards, David E. Heyd

Calculus of A Single Variable 7th Edition solutions

Author: Ron Larson, Robert P. Hostetler, Bruce H. Edwards, David E. Heyd
Publisher: Cengage Learning
ISBN: 9780618149162
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Chapter 9 Problems

Chapter: 9 Problem: 1

Calculus of A Single Variable 7
In Kxercises 1 I, match the eqiiation with (he correct gruph. 1 1 he graphs are labeled (a), (b). (el. and ldl.|

Chapter: 9 Problem: 2

Calculus of A Single Variable 7
In Kxercises 1 I, match the eqiiation with (he correct gruph. 1 1 he graphs are labeled (a), (b). (el. and ldl.|

Chapter: 9 Problem: 3

Calculus of A Single Variable 7
In Kxercises 1 I, match the eqiiation with (he correct gruph. 1 1 he graphs are labeled (a), (b). (el. and ldl.|

Chapter: 9 Problem: 4

Calculus of A Single Variable 7
In Kxercises 1 I, match the eqiiation with (he correct gruph. 1 1 he graphs are labeled (a), (b). (el. and ldl.|

Chapter: 9 Problem: 5

Calculus of A Single Variable 7
In Exercises 5-10, analyze each equation and sketch its graph. Use a graphing utility to conlirni your results. 16.V- + 16y- - 16.V + 24y - .^ =

Chapter: 9 Problem: 6

Calculus of A Single Variable 7
In Exercises 5-10, analyze each equation and sketch its graph. Use a graphing utility to conlirni your results. y-- I2y - 8.v + 20 =

Chapter: 9 Problem: 7

Calculus of A Single Variable 7
In Exercises 5-10, analyze each equation and sketch its graph. Use a graphing utility to conlirni your results. 3.V- - 2y- + 24.V + 12\ + 24 =

Chapter: 9 Problem: 8

Calculus of A Single Variable 7
In Exercises 5-10, analyze each equation and sketch its graph. Use a graphing utility to conlirni your results. .V- + y- - 16.V + 1.5 =

Chapter: 9 Problem: 9

Calculus of A Single Variable 7
In Exercises 5-10, analyze each equation and sketch its graph. Use a graphing utility to conlirni your results. 3.V- + 2y= - 12.V + I2y + 29 =

Chapter: 9 Problem: 10

Calculus of A Single Variable 7
In Exercises 5-10, analyze each equation and sketch its graph. Use a graphing utility to conlirni your results. 4.V- - 4\- - 4.V + 8^ - 1 1 =

Chapter: 9 Problem: 11

Calculus of A Single Variable 7
In Kxercises 1 1 and 12, find an equation of the parabola. Vertex: (0.2); Directrix: \= -^

Chapter: 9 Problem: 12

Calculus of A Single Variable 7
In Kxercises 1 1 and 12, find an equation of the parabola. Vertex: (4.2); Focus: (4.0)

Chapter: 9 Problem: 13

Calculus of A Single Variable 7
In Exercises 13 and 14, find an equation of the ellipse. Vertices: (-3.0). (7.0); Foci: (0.0). (4.0)

Chapter: 9 Problem: 14

Calculus of A Single Variable 7
In Exercises 13 and 14, find an equation of the ellipse.Center: (0. 0): Solution points: ( 1 . 2). (2.01

Chapter: 9 Problem: 15

Calculus of A Single Variable 7
In Kxercises 15 and 16, find an equation of the hyperbola. Vertices: (4.0); Foci: (6.0)

Chapter: 9 Problem: 16

Calculus of A Single Variable 7
In Kxercises 15 and 16, find an equation of the hyperbola. Foci: (0. S); Asymptotes: \' = 4v

Chapter: 9 Problem: 17

Calculus of A Single Variable 7
In Kxercises 17 and IS. use a graphing utilil\ to approximate the perimeter of the ellipse.

Chapter: 9 Problem: 18

Calculus of A Single Variable 7
In Kxercises 17 and IS. use a graphing utilil\ to approximate the perimeter of the ellipse.

Chapter: 9 Problem: 19

Calculus of A Single Variable 7
A line is tangent to the parabola ) = .v- - 2v + 2 and perpendicular to the line y = ,v - 2, Find the equation of the line.

Chapter: 9 Problem: 20

Calculus of A Single Variable 7
Satellite Antenna A cross section of a large parabolic antenna IS modeled by the graph of v = .v7200. - 100 < .v < I(.)0. The receiving and transmitting equipment is positioned at the focus. (a) Find (he coordinates of the focus. (b) Find the surface area of the antenna.

Chapter: 9 Problem: 21

Calculus of A Single Variable 7
Consider a fire truck with a water tank Id led long whose vertical cross sections are ellipses modeled by the equation .V-/16 + i79 = I. (a) Find the volume of the tank. (b) Find the force on the end of the tank when it is full of water. (The density of water is 62.4 pounds per cubic foot. I (c) Fin

Chapter: 9 Problem: 22

Calculus of A Single Variable 7
Consider the region hounded by tlie ellipse eecenlricity c = c/a. (a) Show that the area of the region is -mih. (b) Show that the solid (oblate spheroid) generated by revolv ing the region about the minor axis ol the ellipse has a \olume of I' = 4-irh/?i and a surface area of n=^ 34. S = lira- + m'AJ

Chapter: 9 Problem: 23

Calculus of A Single Variable 7
In Exercises 23-28, sketch the curve represented by the ametric equations (indicate the orientation of the curve). \\ri(e the correspondiii}; rectangular equation by eliminat the parameter..V = I -I- 4(, y = 2 - 3r

Chapter: 9 Problem: 24

Calculus of A Single Variable 7
In Exercises 23-28, sketch the curve represented by the ametric equations (indicate the orientation of the curve). \\ri(e the correspondiii}; rectangular equation by eliminat the parameter..V = / -I- 4, y = t

Chapter: 9 Problem: 25

Calculus of A Single Variable 7
In Exercises 23-28, sketch the curve represented by the ametric equations (indicate the orientation of the curve). \\ri(e the correspondiii}; rectangular equation by eliminat the parameter.V = 6 cos 9, y = 6 sin H

Chapter: 9 Problem: 26

Calculus of A Single Variable 7
In Exercises 23-28, sketch the curve represented by the ametric equations (indicate the orientation of the curve). \\ri(e the correspondiii}; rectangular equation by eliminat the parameter.\ = 3 + 3 cos H. y = 2 + 5 sin

Chapter: 9 Problem: 27

Calculus of A Single Variable 7
In Exercises 23-28, sketch the curve represented by the ametric equations (indicate the orientation of the curve). \\ri(e the correspondiii}; rectangular equation by eliminat the parameter.A = 2 -I- sec 0. y = 3 + tan H

Chapter: 9 Problem: 28

Calculus of A Single Variable 7
In Exercises 23-28, sketch the curve represented by the ametric equations (indicate the orientation of the curve). \\ri(e the correspondiii}; rectangular equation by eliminat the parameter.\ = 5 sin-' 0. V = 5 cos' II

Chapter: 9 Problem: 29

Calculus of A Single Variable 7
In Kxercises 29-32. lind a parametric representation of the hne or conic. Lnic: Passes thioLigh ( - 2. h) and

Chapter: 9 Problem: 30

Calculus of A Single Variable 7
In Kxercises 29-32. lind a parametric representation of the hne or conic. Lnic: Passes thioLigh ( - 2. h) and

Chapter: 9 Problem: 31

Calculus of A Single Variable 7
In Kxercises 29-32. lind a parametric representation of the hne or conic. Ellipse: Center at (-3,4); Horizontal major axis of length iS and niHior axis of length h

Chapter: 9 Problem: 32

Calculus of A Single Variable 7
In Kxercises 29-32. lind a parametric representation of the hne or conic. Hyperbola: Vertices at (0, 4); Foci at (f), 5)

Chapter: 9 Problem: 33

Calculus of A Single Variable 7
Riitaiy Engine The rotary engine was developed by Felix Wankcl in the l'^)5()s (see Chapter 4). It features a rotor, which is a modified equilateral triangle. The mlur mo\es in a chLimber that, in two dimensions, is an epitrochoid. Use a graphing utility to graph the chamber modeled by the parametri

Chapter: 9 Problem: 34

Calculus of A Single Variable 7
A hypocycloid has the parametric equations Use a graphing utility to graph the hypocycloid for each of the following values of a and /'. ^ 35. (a) (( = 2. /) = 1 (b) a = 3. /) == 1 (c) a = 4. b = I (d) a = 10. /. = (e) a = 3. /) =- -) (f) a = 4. b = 3

Chapter: 9 Problem: 35

Calculus of A Single Variable 7
Serpentine Curve Consider the parametric equations .V = 2 cot W and y = 4 sin $ cos H. < < n. (a) U.se a graphing utility to sketch the curve. (b) Eliminate the parameter to show that the rectangular equation of the seipentine curve is (4 + x-)y = 8.v.

Chapter: 9 Problem: 36

Calculus of A Single Variable 7
Involute of a Circle The involute of a circle is described by the endpoint P of a string that is held taut as it is unwound from a spool that does not turn (see figure). Show that a parametric representalion of (he involute is .V = j-(cos H + H sm H) and \' = r(sin - 6 con 0).

Chapter: 9 Problem: 37

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 38

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 39

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 40

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 41

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 42

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 43

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 44

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 45

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 46

Calculus of A Single Variable 7
In Exercises 37-46. (a) find dy/dx and all points of horizontal tangency. (b) eliminate the parameter where possi ble, and (c) sketch the curve represented by the parametric equations.

Chapter: 9 Problem: 47

Calculus of A Single Variable 7
In Exercises 47 and 48. (a) use a graphing utility to sketch the curve represented by the parametric equations, (b) use a graphing utility to find dx/dO. dyjdtt. and dyjdx for = ttJ(\. and (c) use a graphing utility to graph the tangent line to the curve when = 7t/6. .V = cot V = sin 20

Chapter: 9 Problem: 48

Calculus of A Single Variable 7
In Exercises 47 and 48. (a) use a graphing utility to sketch the curve represented by the parametric equations, (b) use a graphing utility to find dx/dO. dyjdtt. and dyjdx for = ttJ(\. and (c) use a graphing utility to graph the tangent line to the curve when = 7t/6. A y 20 - sin 2 - cos

Chapter: 9 Problem: 49

Calculus of A Single Variable 7
In Exercises 49 and 50. find the length of the curve represented by the parametric equations over the given interval. V = r(cos e + (9 sin $) V = /'(sin - 9 cos 0) < e < IT

Chapter: 9 Problem: 50

Calculus of A Single Variable 7
In Exercises 49 and 50. find the length of the curve represented by the parametric equations over the given interval. a = 6 cos H y = 6 sin < e < TT

Chapter: 9 Problem: 51

Calculus of A Single Variable 7
In Exercises 51 and 52. the rectangular coordinates of a point are given. Plot the point and find two sets of polar coor dinates for the point for < < 2tt. (4. -4)

Chapter: 9 Problem: 52

Calculus of A Single Variable 7
In Exercises 51 and 52. the rectangular coordinates of a point are given. Plot the point and find two sets of polar coor dinates for the point for < < 2tt. (-1.3)

Chapter: 9 Problem: 53

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. ( = 3 cos d

Chapter: 9 Problem: 54

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. ) = 10

Chapter: 9 Problem: 55

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. /- = -2(1 + cos d)

Chapter: 9 Problem: 56

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. / cos

Chapter: 9 Problem: 57

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. /- = cos2ff

Chapter: 9 Problem: 58

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. ) = 4 sec| ^

Chapter: 9 Problem: 59

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. ; = 4 cos 2 sec

Chapter: 9 Problem: 60

Calculus of A Single Variable 7
In P^xercises 5.^-60, convert the polar equation to rectangular form. =

Chapter: 9 Problem: 61

Calculus of A Single Variable 7
In Exercises 61-64, convert the rectangular equation to polar form. (a- + y-)- = a.x-y

Chapter: 9 Problem: 62

Calculus of A Single Variable 7
In Exercises 61-64, convert the rectangular equation to polar form. A- + \- - 4 V = A'

Chapter: 9 Problem: 63

Calculus of A Single Variable 7
In Exercises 61-64, convert the rectangular equation to polar form. A- + V- = (V- arctan ' .

Chapter: 9 Problem: 64

Calculus of A Single Variable 7
In Exercises 61-64, convert the rectangular equation to polar form. (a- + V-) arclan

Chapter: 9 Problem: 65

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 66

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 67

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 68

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 69

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 70

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 71

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 72

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 73

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 74

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 75

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 76

Calculus of A Single Variable 7
In Exercises 65-76, sketch a graph of the polar e(|uation.

Chapter: 9 Problem: 77

Calculus of A Single Variable 7
In Exercises 77-80, use a graphing utility to graph the polar equation.

Chapter: 9 Problem: 78

Calculus of A Single Variable 7
In Exercises 77-80, use a graphing utility to graph the polar equation.

Chapter: 9 Problem: 79

Calculus of A Single Variable 7
In Exercises 77-80, use a graphing utility to graph the polar equation.

Chapter: 9 Problem: 80

Calculus of A Single Variable 7
In Exercises 77-80, use a graphing utility to graph the polar equation.

Chapter: 9 Problem: 81

Calculus of A Single Variable 7
In Exercises 81 and 82, (a) find the tangents at the pole, (b) find all points of horizontal and vertical tangency. and (c) use a graphing utility to graph the polar equation and draw a tangent line to the graph for = tjJ6. )- = 1 - 2 cos

Chapter: 9 Problem: 82

Calculus of A Single Variable 7
In Exercises 81 and 82, (a) find the tangents at the pole, (b) find all points of horizontal and vertical tangency. and (c) use a graphing utility to graph the polar equation and draw a tangent line to the graph for = tjJ6. ;- = 4 sin 20

Chapter: 9 Problem: 83

Calculus of A Single Variable 7
Pmd the angle between the circle r = 3 sm and the liniac^on I- = 4 - 5 sin at tlie punit of intersection (3/2. Tr/6).

Chapter: 9 Problem: 84

Calculus of A Single Variable 7
True or False? There is a unique polar coordinate represen lalion tor each point in the plane. Hxpiain,

Chapter: 9 Problem: 85

Calculus of A Single Variable 7
I" Exercises 85 and 86, show that the graphs of the polar equations arc orthogonal at the points of intersection. Use a graphing utility to confirm your results graphically. ; = 1 + cos r = \ - cos

Chapter: 9 Problem: 86

Calculus of A Single Variable 7
I" Exercises 85 and 86, show that the graphs of the polar equations arc orthogonal at the points of intersection. Use a graphing utility to confirm your results graphically. a sin CI cos

Chapter: 9 Problem: 87

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places.

Chapter: 9 Problem: 88

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places.

Chapter: 9 Problem: 89

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places.

Chapter: 9 Problem: 90

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places.

Chapter: 9 Problem: 91

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places. Interior of r- = 4 sin 20

Chapter: 9 Problem: 92

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places. Common interior of r = 3 and r- = IS sin 2(*

Chapter: 9 Problem: 93

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places. Common interior of / = 4 cos Wand / - 2

Chapter: 9 Problem: 94

Calculus of A Single Variable 7
In Exercises S7-94. use a graphing utility to graph the polar equation. Set up an integral for finding the area of the indicated region and use the integration capabilities of a graphing utility to approximate the integral accurate to two decimal places. Reiiion bounded by the polar axis and c = c"

Chapter: 9 Problem: 95

Calculus of A Single Variable 7
In Exercises 95 and 96. find the perimeter of the curve.

Chapter: 9 Problem: 96

Calculus of A Single Variable 7
In Exercises 95 and 96. find the perimeter of the curve.

Chapter: 9 Problem: 97

Calculus of A Single Variable 7
In Exercises 97-102. sketch and identify the graph. Use a graphing utilit\ to confirm your results.

Chapter: 9 Problem: 98

Calculus of A Single Variable 7
In Exercises 97-102. sketch and identify the graph. Use a graphing utilit\ to confirm your results.

Chapter: 9 Problem: 99

Calculus of A Single Variable 7
In Exercises 97-102. sketch and identify the graph. Use a graphing utilit\ to confirm your results.

Chapter: 9 Problem: 100

Calculus of A Single Variable 7
In Exercises 97-102. sketch and identify the graph. Use a graphing utilit\ to confirm your results.

Chapter: 9 Problem: 101

Calculus of A Single Variable 7
In Exercises 97-102. sketch and identify the graph. Use a graphing utilit\ to confirm your results.

Chapter: 9 Problem: 102

Calculus of A Single Variable 7
In Exercises 97-102. sketch and identify the graph. Use a graphing utilit\ to confirm your results.

Chapter: 9 Problem: 103

Calculus of A Single Variable 7
In Exercises 10.3-108, find a polar equation for the line or conic. Circle Circle Solution point: (0. 0)

Chapter: 9 Problem: 104

Calculus of A Single Variable 7
In Exercises 10.3-108, find a polar equation for the line or conic. 1 ine Solution point; (0,0) Slope; y3

Chapter: 9 Problem: 105

Calculus of A Single Variable 7
In Exercises 10.3-108, find a polar equation for the line or conic. Parabola Vertex; (2. n) Focus; (0, 0)

Chapter: 9 Problem: 106

Calculus of A Single Variable 7
In Exercises 10.3-108, find a polar equation for the line or conic. Parabola Vertex: (2. tt/2) Focus; (0. 0)

Chapter: 9 Problem: 107

Calculus of A Single Variable 7
In Exercises 10.3-108, find a polar equation for the line or conic. Ellipse Vertices; (5.0). (I.ttOne focus: (0. 0)

Chapter: 9 Problem: 108

Calculus of A Single Variable 7
In Exercises 10.3-108, find a polar equation for the line or conic. Hyperbola Vertices: (1.0). (7.0) One focus; (0, 0)

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