Calculus: Early Transcendental Functions
7th Edition
ISBN: 9781337552516
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Chapter 13.9, Problem 17E
To determine
To prove: The highest proportion of population that could be heterozygous is
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Calculus: Early Transcendental Functions
Ch. 13.1 - Think About It Explain why z2=x+3y is not a...Ch. 13.1 - Function of Two Variables What is a graph of a...Ch. 13.1 - Determine whether graph is a function. Use the...Ch. 13.1 - Contour Map Explain how to sketch a contour map of...Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...
Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Evaluating a Function In Exercises 9-20, evaluate...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Finding the Domain and Range of a Function In...Ch. 13.1 - Think About It The graphs labeled (a), (b). (c)....Ch. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - Sketching a Surface In Exercises 35-42, describe...Ch. 13.1 - Prob. 38ECh. 13.1 - Prob. 39ECh. 13.1 - Prob. 40ECh. 13.1 - Prob. 41ECh. 13.1 - Sketching a Surface In Exercises 35-42, describe...Ch. 13.1 - Graphing a Function Using Technology In Exercises...Ch. 13.1 - Graphing a Function Using Technology In Exercises...Ch. 13.1 - Graphing a Function Using Technology In Exercises...Ch. 13.1 - Graphing a Function Using Technology In Exercises...Ch. 13.1 - Matching In Exercises 47-50, match the graph of...Ch. 13.1 - Matching In Exercises 47-50, match the graph of...Ch. 13.1 - Matching In Exercises 47-50, match the graph of...Ch. 13.1 - Matching In Exercises 47-50, match the graph of...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Sketching a Contour Map In Exercises 51-58,...Ch. 13.1 - Graphing Level Curves Using Technology In...Ch. 13.1 - Graphing Level Curves Using Technology In...Ch. 13.1 - Graphing Level Curves Using Technology In...Ch. 13.1 - Graphing Level Curves Using Technology In...Ch. 13.1 - Vertical Line Test Does die Vertical Line Test...Ch. 13.1 - Using Level Curves All of the level curves of the...Ch. 13.1 - Creating a Function Construct a function whose...Ch. 13.1 - Conjecture Consider the function f(x,y)=xy, for...Ch. 13.1 - Writing In Exercises 67 and 68, use the graphs of...Ch. 13.1 - Writing In Exercises 67 and 68, use the graphs of...Ch. 13.1 - Investment In 2016, an investment of S1000 was...Ch. 13.1 - Investment A principal of $5000 is deposited in a...Ch. 13.1 - Sketching a Level Surface In Exercises 71-76....Ch. 13.1 - Sketching a Level Surface In Exercises 71-76....Ch. 13.1 - Sketching a Level Surface In Exercises 71-76....Ch. 13.1 - Sketching a Level Surface In Exercises 71-76....Ch. 13.1 - Sketching a Level Surface In Exercises 71-76....Ch. 13.1 - Sketching a Level Surface In Exercises 71-76....Ch. 13.1 - Forestry The Doyle Lux Rule is one of several...Ch. 13.1 - Queuing Model The average length of time that a...Ch. 13.1 - Temperature Distribution The temperature T (in...Ch. 13.1 - Electric Potential The electric potential V at any...Ch. 13.1 - Prob. 81ECh. 13.1 - Cobb-Douglas Production Function In Exercises 81...Ch. 13.1 - Prob. 83ECh. 13.1 - Cobb-Douglas Production Function Show that the...Ch. 13.1 - Ideal Gas Law According to the Ideal Gas Law, PV=...Ch. 13.1 - Prob. 86ECh. 13.1 - Prob. 87ECh. 13.1 - Acid Rain The acidity of rainwater is measured in...Ch. 13.1 - Prob. 89ECh. 13.1 - HOW DO YOU SEE IT? The contour map of the Southern...Ch. 13.1 - Prob. 91ECh. 13.1 - Prob. 92ECh. 13.1 - Prob. 93ECh. 13.1 - Prob. 94ECh. 13.1 - Prob. 95ECh. 13.2 - CONCEPT CHECK Describing Notation Write a brief...Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Verifying a Limit by the Definition In Exercises...Ch. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Prob. 25ECh. 13.2 - Prob. 26ECh. 13.2 - Finding a Limit In Exercises 25-36, find the limit...Ch. 13.2 - Prob. 28ECh. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Prob. 41ECh. 13.2 - Prob. 42ECh. 13.2 - Prob. 43ECh. 13.2 - Prob. 44ECh. 13.2 - Prob. 45ECh. 13.2 - Prob. 46ECh. 13.2 - Limit Consider lim(x,y)(0,0)x2+y2xy (see figure)....Ch. 13.2 - Prob. 48ECh. 13.2 - Prob. 49ECh. 13.2 - Prob. 50ECh. 13.2 - Prob. 51ECh. 13.2 - Prob. 52ECh. 13.2 - Prob. 53ECh. 13.2 - Prob. 54ECh. 13.2 - Prob. 55ECh. 13.2 - Prob. 56ECh. 13.2 - Prob. 57ECh. 13.2 - Prob. 58ECh. 13.2 - Finding a Limit Using Polar Coordinates In...Ch. 13.2 - Finding a Limit Using Polar Coordinates In...Ch. 13.2 - Prob. 61ECh. 13.2 - Prob. 62ECh. 13.2 - Continuity In Exercises 61-66, discuss the...Ch. 13.2 - Continuity In Exercises 61-66, discuss the...Ch. 13.2 - Prob. 65ECh. 13.2 - Prob. 66ECh. 13.2 - Prob. 67ECh. 13.2 - Prob. 68ECh. 13.2 - Prob. 69ECh. 13.2 - Prob. 70ECh. 13.2 - Prob. 71ECh. 13.2 - Prob. 72ECh. 13.2 - Prob. 73ECh. 13.2 - Prob. 74ECh. 13.2 - Finding a Limit In Exercises 71-76, find each...Ch. 13.2 - Finding a Limit In Exercises 71-76, find each...Ch. 13.2 - Finding a Limit Using Spherical Coordinates In...Ch. 13.2 - Finding a Limit Using Spherical Coordinates In...Ch. 13.2 - Prob. 79ECh. 13.2 - True or False? In Exercises 79-82, determine...Ch. 13.2 - Prob. 81ECh. 13.2 - Prob. 82ECh. 13.2 - Prob. 83ECh. 13.2 - Prob. 84ECh. 13.2 - Prob. 85ECh. 13.2 - Prob. 86ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - Prob. 30ECh. 13.3 - Prob. 31ECh. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - Prob. 37ECh. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - Prob. 40ECh. 13.3 - Prob. 41ECh. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - Prob. 49ECh. 13.3 - Prob. 50ECh. 13.3 - Prob. 51ECh. 13.3 - Prob. 52ECh. 13.3 - Prob. 53ECh. 13.3 - Prob. 54ECh. 13.3 - Prob. 55ECh. 13.3 - Prob. 56ECh. 13.3 - Prob. 57ECh. 13.3 - Prob. 58ECh. 13.3 - Prob. 59ECh. 13.3 - Prob. 60ECh. 13.3 - Prob. 61ECh. 13.3 - Prob. 62ECh. 13.3 - Prob. 63ECh. 13.3 - Prob. 64ECh. 13.3 - Prob. 65ECh. 13.3 - Prob. 66ECh. 13.3 - Prob. 67ECh. 13.3 - Prob. 68ECh. 13.3 - Prob. 69ECh. 13.3 - Prob. 70ECh. 13.3 - Prob. 71ECh. 13.3 - Prob. 72ECh. 13.3 - Prob. 73ECh. 13.3 - Prob. 74ECh. 13.3 - Prob. 75ECh. 13.3 - Prob. 76ECh. 13.3 - Prob. 77ECh. 13.3 - Prob. 78ECh. 13.3 - Prob. 79ECh. 13.3 - Prob. 80ECh. 13.3 - Prob. 81ECh. 13.3 - Prob. 82ECh. 13.3 - Prob. 83ECh. 13.3 - Prob. 84ECh. 13.3 - Prob. 85ECh. 13.3 - Prob. 86ECh. 13.3 - Prob. 87ECh. 13.3 - Prob. 88ECh. 13.3 - Prob. 89ECh. 13.3 - Prob. 90ECh. 13.3 - Prob. 91ECh. 13.3 - Prob. 92ECh. 13.3 - Prob. 93ECh. 13.3 - Prob. 94ECh. 13.3 - Prob. 95ECh. 13.3 - Prob. 96ECh. 13.3 - Prob. 97ECh. 13.3 - Prob. 98ECh. 13.3 - Prob. 99ECh. 13.3 - Wave Equation In Exercises 99-102, show that the...Ch. 13.3 - Prob. 101ECh. 13.3 - Prob. 102ECh. 13.3 - Heat Equation In Exercises 103 and 104, show that...Ch. 13.3 - Prob. 104ECh. 13.3 - Prob. 105ECh. 13.3 - Cauchy-Riemann Equations In Exercises 105 and 106,...Ch. 13.3 - Prob. 107ECh. 13.3 - Prob. 108ECh. 13.3 - Prob. 109ECh. 13.3 - Prob. 110ECh. 13.3 - Prob. 111ECh. 13.3 - Prob. 112ECh. 13.3 - Prob. 113ECh. 13.3 - Prob. 114ECh. 13.3 - Prob. 115ECh. 13.3 - Prob. 116ECh. 13.3 - Prob. 117ECh. 13.3 - Prob. 118ECh. 13.3 - Prob. 119ECh. 13.3 - Prob. 120ECh. 13.3 - Prob. 121ECh. 13.3 - Investment The value of an investment of $1000...Ch. 13.3 - Prob. 123ECh. 13.3 - Apparent Temperature A measure of how hot weather...Ch. 13.3 - Prob. 125ECh. 13.3 - Prob. 126ECh. 13.3 - Prob. 127ECh. 13.3 - Prob. 128ECh. 13.3 - Prob. 129ECh. 13.3 - Prob. 130ECh. 13.3 - Prob. 131ECh. 13.4 - CONCEPT CHECK Approximation Describe the change in...Ch. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Finding a Total Differential find the total...Ch. 13.4 - Finding a Total Differential find the total...Ch. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Using a Differential as an Approximation In...Ch. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 14ECh. 13.4 - Approximating an Expression In Exercises 15-18,...Ch. 13.4 - Prob. 16ECh. 13.4 - Approximating an Expression In Exercises 15-18,...Ch. 13.4 - Prob. 18ECh. 13.4 - Continuity If fx. and fy are each continuous in an...Ch. 13.4 - Prob. 20ECh. 13.4 - Prob. 21ECh. 13.4 - Volume The volume of the red right circular...Ch. 13.4 - Prob. 23ECh. 13.4 - Volume The possible error involved in measuring...Ch. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Wind Chill The formula for wind chill C (in...Ch. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Volume A trough is 16 feet long (see figure). Its...Ch. 13.4 - Sports A baseball player in center field is...Ch. 13.4 - Inductance The inductance L (in microhenrys) of a...Ch. 13.4 - Prob. 34ECh. 13.4 - Prob. 35ECh. 13.4 - Prob. 36ECh. 13.4 - Prob. 37ECh. 13.4 - Differentiability In Exercises 35-38, show that...Ch. 13.4 - Prob. 39ECh. 13.4 - Differentiability In Exercises 39 and 40, use the...Ch. 13.5 - Prob. 1ECh. 13.5 - Prob. 2ECh. 13.5 - Using the Chain Rule In Exercises 3-6, find dw/dt...Ch. 13.5 - Using the Chain Rule In Exercises 3-6, find dw/dt...Ch. 13.5 - Using the Chain Rule In Exercises 3-6, find dw/dt...Ch. 13.5 - Using the Chain Rule In Exercises 3-6, find dw/dt...Ch. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Using Different Methods In Exercises 7-12, find...Ch. 13.5 - Using Different Methods In Exercises 7-12, find...Ch. 13.5 - Prob. 11ECh. 13.5 - Using Different Methods In Exercises 7-12, find...Ch. 13.5 - Projectile Motion In Exercises 13 and 14, the...Ch. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 18ECh. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Using Different Methods In Exercises 19-22, find...Ch. 13.5 - Prob. 23ECh. 13.5 - Prob. 24ECh. 13.5 - Prob. 25ECh. 13.5 - Finding a Derivative Implicitly In Exercises...Ch. 13.5 - Prob. 27ECh. 13.5 - Prob. 28ECh. 13.5 - Prob. 29ECh. 13.5 - Prob. 30ECh. 13.5 - Prob. 31ECh. 13.5 - Prob. 32ECh. 13.5 - Prob. 33ECh. 13.5 - Prob. 34ECh. 13.5 - Prob. 35ECh. 13.5 - Prob. 36ECh. 13.5 - Prob. 37ECh. 13.5 - Prob. 38ECh. 13.5 - Prob. 39ECh. 13.5 - Prob. 40ECh. 13.5 - Homogeneous Functions A function f is homogeneous...Ch. 13.5 - Prob. 42ECh. 13.5 - Using a Table of Values Let w=f(x,y),x=g(t), and...Ch. 13.5 - Prob. 44ECh. 13.5 - Prob. 45ECh. 13.5 - Prob. 46ECh. 13.5 - Prob. 47ECh. 13.5 - HOW DO YOU SEE IT? The path of an object...Ch. 13.5 - Prob. 49ECh. 13.5 - Prob. 50ECh. 13.5 - Moment of Inertia An annular cylinder has an...Ch. 13.5 - Volume and Surface Area The two radii of the...Ch. 13.5 - Prob. 53ECh. 13.5 - Cauchy-Riemann Equations Demonstrate the result of...Ch. 13.5 - Prob. 55ECh. 13.6 - CONCEPT CHECK Directional Derivative For a...Ch. 13.6 - Prob. 2ECh. 13.6 - Prob. 3ECh. 13.6 - Prob. 4ECh. 13.6 - Prob. 5ECh. 13.6 - Prob. 6ECh. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Prob. 12ECh. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Finding the Gradient of a Function In Exercises...Ch. 13.6 - Prob. 18ECh. 13.6 - Prob. 19ECh. 13.6 - Prob. 20ECh. 13.6 - Prob. 21ECh. 13.6 - Prob. 22ECh. 13.6 - Prob. 23ECh. 13.6 - Prob. 24ECh. 13.6 - Prob. 25ECh. 13.6 - Prob. 26ECh. 13.6 - Prob. 27ECh. 13.6 - Prob. 28ECh. 13.6 - Prob. 29ECh. 13.6 - Prob. 30ECh. 13.6 - Using Properties of the Gradient In Exercises...Ch. 13.6 - Prob. 32ECh. 13.6 - Prob. 33ECh. 13.6 - Prob. 34ECh. 13.6 - Using Properties of the Gradient In Exercises...Ch. 13.6 - Prob. 36ECh. 13.6 - Prob. 37ECh. 13.6 - Prob. 38ECh. 13.6 - Prob. 39ECh. 13.6 - Prob. 40ECh. 13.6 - Prob. 41ECh. 13.6 - Prob. 42ECh. 13.6 - Prob. 43ECh. 13.6 - Prob. 44ECh. 13.6 - Prob. 45ECh. 13.6 - Prob. 46ECh. 13.6 - Using a Function Consider the function...Ch. 13.6 - Prob. 48ECh. 13.6 - Prob. 49ECh. 13.6 - Prob. 50ECh. 13.6 - Prob. 51ECh. 13.6 - Prob. 52ECh. 13.6 - Topography The surface of a mountain is modeled by...Ch. 13.6 - Prob. 54ECh. 13.6 - Temperature The temperature at the point (x, y) on...Ch. 13.6 - Prob. 56ECh. 13.6 - Prob. 57ECh. 13.6 - Prob. 58ECh. 13.6 - Prob. 59ECh. 13.6 - Finding the Path of a Heat-Seeking Particle In...Ch. 13.6 - Prob. 61ECh. 13.6 - True or False? In Exercises 61-64, determine...Ch. 13.6 - Prob. 63ECh. 13.6 - Prob. 64ECh. 13.6 - Prob. 65ECh. 13.6 - Ocean Floor A team of oceanographers is mapping...Ch. 13.6 - Prob. 67ECh. 13.6 - Prob. 68ECh. 13.7 - CONCEPT CHECK Tangent Vector Consider a point...Ch. 13.7 - Prob. 2ECh. 13.7 - Describing a Surface In Exercises 3-6, describe...Ch. 13.7 - Prob. 4ECh. 13.7 - Describing a Surface In Exercises 3-6, describe...Ch. 13.7 - Describing a Surface In Exercises 3-6, describe...Ch. 13.7 - Finding an Equation of a Tangent Plane In...Ch. 13.7 - Finding an Equation of a Tangent Plane In...Ch. 13.7 - Finding an Equation of a Tangent Plane In...Ch. 13.7 - Prob. 10ECh. 13.7 - Finding an Equation of a Tangent Plane In...Ch. 13.7 - Finding an Equation of a Tangent Plane In...Ch. 13.7 - Prob. 13ECh. 13.7 - Prob. 14ECh. 13.7 - Prob. 15ECh. 13.7 - Prob. 16ECh. 13.7 - Finding an Equation of a Tangent Plane and a...Ch. 13.7 - Prob. 18ECh. 13.7 - Finding an Equation of a Tangent Plane and a...Ch. 13.7 - Prob. 20ECh. 13.7 - Prob. 21ECh. 13.7 - Finding an Equation of a Tangent Plane and a...Ch. 13.7 - Finding an Equation of a Tangent Plane and a...Ch. 13.7 - Prob. 24ECh. 13.7 - Prob. 25ECh. 13.7 - Prob. 26ECh. 13.7 - Prob. 27ECh. 13.7 - Prob. 28ECh. 13.7 - Finding the Equation of a Tangent Line to a Curve...Ch. 13.7 - Prob. 30ECh. 13.7 - Finding the Equation of a Tangent Line to a Curve...Ch. 13.7 - Prob. 32ECh. 13.7 - Prob. 33ECh. 13.7 - Prob. 34ECh. 13.7 - Finding the Angle of Inclination of a Tangent...Ch. 13.7 - Prob. 36ECh. 13.7 - Prob. 37ECh. 13.7 - Horizontal Tangent Plane In Exercises 37-42, find...Ch. 13.7 - Prob. 39ECh. 13.7 - Prob. 40ECh. 13.7 - Prob. 41ECh. 13.7 - Prob. 42ECh. 13.7 - Tangent Surfaces In Exercises 43 and 44, show that...Ch. 13.7 - Prob. 44ECh. 13.7 - Prob. 45ECh. 13.7 - Prob. 46ECh. 13.7 - Prob. 47ECh. 13.7 - Prob. 48ECh. 13.7 - Prob. 49ECh. 13.7 - Prob. 50ECh. 13.7 - Using an Ellipsoid Find a point on the ellipsoid...Ch. 13.7 - Prob. 52ECh. 13.7 - Prob. 53ECh. 13.7 - Prob. 54ECh. 13.7 - Prob. 55ECh. 13.7 - Prob. 56ECh. 13.7 - Prob. 57ECh. 13.7 - Prob. 58ECh. 13.7 - Prob. 59ECh. 13.7 - Tangent Planes Let f be a differentiable function...Ch. 13.7 - Prob. 61ECh. 13.7 - Approximation Repeat Exercise 61 for the function...Ch. 13.7 - Prob. 63ECh. 13.7 - Prob. 64ECh. 13.8 - CONCEPT CHECK Function of Two Variables For a...Ch. 13.8 - Prob. 2ECh. 13.8 - Prob. 3ECh. 13.8 - Prob. 4ECh. 13.8 - Prob. 5ECh. 13.8 - Prob. 6ECh. 13.8 - Prob. 7ECh. 13.8 - Prob. 8ECh. 13.8 - Prob. 9ECh. 13.8 - Prob. 10ECh. 13.8 - Prob. 11ECh. 13.8 - Prob. 12ECh. 13.8 - Prob. 13ECh. 13.8 - Prob. 14ECh. 13.8 - Prob. 15ECh. 13.8 - Prob. 16ECh. 13.8 - Prob. 17ECh. 13.8 - Prob. 18ECh. 13.8 - Prob. 19ECh. 13.8 - Prob. 20ECh. 13.8 - Prob. 21ECh. 13.8 - Prob. 22ECh. 13.8 - Prob. 23ECh. 13.8 - Prob. 24ECh. 13.8 - Prob. 25ECh. 13.8 - Prob. 26ECh. 13.8 - Prob. 27ECh. 13.8 - Prob. 28ECh. 13.8 - Prob. 29ECh. 13.8 - Prob. 30ECh. 13.8 - Prob. 31ECh. 13.8 - Prob. 32ECh. 13.8 - Prob. 33ECh. 13.8 - Prob. 34ECh. 13.8 - Prob. 35ECh. 13.8 - Prob. 36ECh. 13.8 - Prob. 37ECh. 13.8 - Prob. 38ECh. 13.8 - Prob. 39ECh. 13.8 - Prob. 40ECh. 13.8 - Prob. 41ECh. 13.8 - Prob. 42ECh. 13.8 - Prob. 43ECh. 13.8 - Finding Absolute Extrema In Exercises 39-46, find...Ch. 13.8 - Prob. 45ECh. 13.8 - Prob. 46ECh. 13.8 - Examining a Function In Exercises 47 and 48, find...Ch. 13.8 - Prob. 48ECh. 13.8 - Prob. 49ECh. 13.8 - Prob. 50ECh. 13.8 - Prob. 51ECh. 13.8 - Prob. 52ECh. 13.8 - Prob. 53ECh. 13.8 - Prob. 54ECh. 13.8 - True or False? In Exercises 55-58, determine...Ch. 13.8 - Prob. 56ECh. 13.8 - Prob. 57ECh. 13.8 - Prob. 58ECh. 13.9 - CONCEPT CHECK Applied Optimization Problems In...Ch. 13.9 - Prob. 2ECh. 13.9 - Prob. 3ECh. 13.9 - Prob. 4ECh. 13.9 - Prob. 5ECh. 13.9 - Prob. 6ECh. 13.9 - Prob. 7ECh. 13.9 - Prob. 8ECh. 13.9 - Finding Positive Numbers In Exercises 7-10, find...Ch. 13.9 - Finding Positive Numbers In Exercises 7-10, find...Ch. 13.9 - Cost A home improvement contractor is painting the...Ch. 13.9 - Maximum Volume The material for constructing the...Ch. 13.9 - Prob. 13ECh. 13.9 - Maximum Volume Show that the rectangular box of...Ch. 13.9 - Prob. 15ECh. 13.9 - Prob. 16ECh. 13.9 - Prob. 17ECh. 13.9 - Shannon Diversity Index One way to measure species...Ch. 13.9 - Minimum Cost A water line is to be built from...Ch. 13.9 - Area A trough with trapezoidal cross sections is...Ch. 13.9 - Prob. 21ECh. 13.9 - Prob. 22ECh. 13.9 - Prob. 23ECh. 13.9 - Prob. 24ECh. 13.9 - Prob. 25ECh. 13.9 - Finding the Least Squares Regression Line In...Ch. 13.9 - Prob. 27ECh. 13.9 - Prob. 28ECh. 13.9 - Prob. 29ECh. 13.9 - Prob. 30ECh. 13.9 - Prob. 31ECh. 13.9 - HOW DO YOU SEE IT? Match the regression equation...Ch. 13.9 - Prob. 33ECh. 13.9 - Prob. 34ECh. 13.9 - Prob. 35ECh. 13.9 - Prob. 36ECh. 13.9 - Prob. 37ECh. 13.9 - Prob. 38ECh. 13.9 - Prob. 39ECh. 13.9 - Prob. 40ECh. 13.9 - Prob. 41ECh. 13.10 - CONCEPT CHECK Constrained Optimization Problems...Ch. 13.10 - Prob. 2ECh. 13.10 - Prob. 3ECh. 13.10 - Prob. 4ECh. 13.10 - Prob. 5ECh. 13.10 - Prob. 6ECh. 13.10 - Using Lagrange Multipliers In Exercises 3-10. use...Ch. 13.10 - Prob. 8ECh. 13.10 - Prob. 9ECh. 13.10 - Prob. 10ECh. 13.10 - Prob. 11ECh. 13.10 - Prob. 12ECh. 13.10 - Prob. 13ECh. 13.10 - Prob. 14ECh. 13.10 - Prob. 15ECh. 13.10 - Prob. 16ECh. 13.10 - Prob. 17ECh. 13.10 - Prob. 18ECh. 13.10 - Prob. 19ECh. 13.10 - Prob. 20ECh. 13.10 - Prob. 21ECh. 13.10 - Prob. 22ECh. 13.10 - Prob. 23ECh. 13.10 - Prob. 24ECh. 13.10 - Prob. 25ECh. 13.10 - Finding Minimum Distance In Exercises 19-28, use...Ch. 13.10 - Prob. 27ECh. 13.10 - Prob. 28ECh. 13.10 - Prob. 29ECh. 13.10 - Prob. 30ECh. 13.10 - Using Lagrange Multipliers In Exercises 31-38, use...Ch. 13.10 - Prob. 32ECh. 13.10 - Prob. 33ECh. 13.10 - Prob. 34ECh. 13.10 - Using Lagrange Multipliers In Exercises 31-38, use...Ch. 13.10 - Prob. 36ECh. 13.10 - Prob. 37ECh. 13.10 - Prob. 38ECh. 13.10 - Prob. 39ECh. 13.10 - Prob. 40ECh. 13.10 - EXPLORING CONCEPTS Method of Lagrange Multipliers...Ch. 13.10 - Prob. 42ECh. 13.10 - Minimum Cost A cargo container (in the shape of a...Ch. 13.10 - Geometric and Arithmetic Means (a) Use Lagrange...Ch. 13.10 - Prob. 45ECh. 13.10 - Prob. 46ECh. 13.10 - Prob. 47ECh. 13.10 - Prob. 48ECh. 13.10 - Prob. 49ECh. 13.10 - Prob. 50ECh. 13.10 - Prob. 51ECh. 13.10 - Prob. 52ECh. 13.10 - A can buoy is to be made of three pieces, namely,...Ch. 13 - Evaluating a Function In Exercises 1 and 2,...Ch. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Finding the Domain and Range of a Function In...Ch. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Sketching a Contour Map In Exercises 7 and 8,...Ch. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Finding the Slopes of a Surface Find the slopes of...Ch. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - Prob. 39RECh. 13 - Prob. 40RECh. 13 - Using a Differential as an Approximation In...Ch. 13 - Prob. 42RECh. 13 - Volume The possible error involved in measuring...Ch. 13 - Prob. 44RECh. 13 - Prob. 45RECh. 13 - Prob. 46RECh. 13 - Prob. 47RECh. 13 - Prob. 48RECh. 13 - Using Different Methods In Exercises 47-50, find...Ch. 13 - Prob. 50RECh. 13 - Prob. 51RECh. 13 - Prob. 52RECh. 13 - Prob. 53RECh. 13 - Prob. 54RECh. 13 - Prob. 55RECh. 13 - Prob. 56RECh. 13 - Prob. 57RECh. 13 - Prob. 58RECh. 13 - Prob. 59RECh. 13 - Prob. 60RECh. 13 - Prob. 61RECh. 13 - Prob. 62RECh. 13 - Prob. 63RECh. 13 - Prob. 64RECh. 13 - Prob. 65RECh. 13 - Using Properties of the Gradient In Exercises...Ch. 13 - Prob. 67RECh. 13 - Prob. 68RECh. 13 - Prob. 69RECh. 13 - Prob. 70RECh. 13 - Prob. 71RECh. 13 - Prob. 72RECh. 13 - Prob. 73RECh. 13 - Prob. 74RECh. 13 - Finding the Angle of Inclination of a Tangent...Ch. 13 - Prob. 76RECh. 13 - Prob. 77RECh. 13 - Prob. 78RECh. 13 - Prob. 79RECh. 13 - Prob. 80RECh. 13 - Prob. 81RECh. 13 - Prob. 82RECh. 13 - Prob. 83RECh. 13 - Prob. 84RECh. 13 - Prob. 85RECh. 13 - Prob. 86RECh. 13 - Prob. 87RECh. 13 - Prob. 88RECh. 13 - Finding the Least Squares Regression Line In...Ch. 13 - Prob. 90RECh. 13 - Prob. 91RECh. 13 - Prob. 92RECh. 13 - Prob. 93RECh. 13 - Using Lagrange Multipliers In Exercises 93-98, use...Ch. 13 - Prob. 95RECh. 13 - Prob. 96RECh. 13 - Prob. 97RECh. 13 - Prob. 98RECh. 13 - Minimum Cost A water line is to be built from...Ch. 13 - Area Herons Formula states that the area of a...Ch. 13 - Minimizing Material An industrial container is in...Ch. 13 - Tangent Plane Let P(x0,y0,z0) be a point in the...Ch. 13 - Prob. 4PSCh. 13 - Prob. 5PSCh. 13 - Minimizing Costs A heated storage room has the...Ch. 13 - Prob. 7PSCh. 13 - Temperature Consider a circular plate of radius 1...Ch. 13 - Prob. 9PSCh. 13 - Minimizing Area Consider the ellipse x2a2+y2b2=1...Ch. 13 - Prob. 11PSCh. 13 - Prob. 12PSCh. 13 - Prob. 13PSCh. 13 - Prob. 14PSCh. 13 - Prob. 15PSCh. 13 - Tangent Planes Let f be a differentiable function...Ch. 13 - Prob. 17PSCh. 13 - Prob. 18PSCh. 13 - Prob. 19PSCh. 13 - Prob. 20PSCh. 13 - Prob. 21PS
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- Conditional probability If 40 of the population have completed college, and 85 of college graduates are registered to vote, what percent of the population are both college graduates and registered voters?arrow_forwardPopulation Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?arrow_forwardPopulation Genetics-First Cousins This is a continuation of Exercise 5. Double first cousins are first cousins in two waysthat is, each of the parents of one is a sibling of a parent of the other. First cousins in general have six different grandparents whereas double first cousins have only four different grandparents. For mating between double first cousins, the proportions of the genotypes of the children can be accounted for in terms of those of parents, grandparents, and great-grandparent: 3=122+14+18. a. Find all solutions to the cubic equation above and Identify which is 1. b. After 5 generations, what proportion of the population will be homozygous? c. After 20 generations, what proportion of the population will be homozygous? 5. Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?arrow_forward
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