Calculus of a Single Variable
11th Edition
ISBN: 9781337275361
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Textbook Question
Chapter 10.1, Problem 35E
Finding the Standard Equation of an Ellipse In Exercises 31–36, find the standard form of the equation of the ellipse with the given characteristics.
Center: (0,0)
Major axis: horizontal
Points on the ellipse: (3, 1). (4, 0)
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Chapter 10 Solutions
Calculus of a Single Variable
Ch. 10.1 - Conic Sections State the definitions of parabola,...Ch. 10.1 - Reflective Property Use a sketch to illustrate the...Ch. 10.1 - Eccentricity Consider an ellipse with eccentricity...Ch. 10.1 - Hyperbola Explain how to sketch a hyperbola with a...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...
Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...Ch. 10.1 - Finding the Standard Equation of a Parabola In...Ch. 10.1 - Finding the Standard Equation of a Parabola In...Ch. 10.1 - Finding the Standard Equation of a Parabola In...Ch. 10.1 - Find the standard form of the equation of parabola...Ch. 10.1 - Finding the Standard Equation of a Parabola In...Ch. 10.1 - Finding the Standard Equation of a Parabola In...Ch. 10.1 - Finding the Standard Equation of a Parabola In...Ch. 10.1 - Finding the Standard Equation of a Parabola In...Ch. 10.1 - Sketching an Ellipse In Exercises 2530, find the...Ch. 10.1 - Sketching an Ellipse In Exercises 2530, find the...Ch. 10.1 - Sketching an Ellipse In Exercises 2530, find the...Ch. 10.1 - Sketching an Ellipse In Exercises 2530, find the...Ch. 10.1 - Prob. 29ECh. 10.1 - Sketching an Ellipse In Exercises 2530, find the...Ch. 10.1 - Finding the Standard Equation of an Ellipse In...Ch. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Finding the Standard Equation of an Ellipse In...Ch. 10.1 - Finding the Standard Equation of an Ellipse In...Ch. 10.1 - Finding the Standard Equation of an Ellipse In...Ch. 10.1 - Sketching a Hyperbola In Exercises 37-40, find the...Ch. 10.1 - Sketching a Hyperbola In Exercises 37-40, find the...Ch. 10.1 - Sketching a Hyperbola In Exercises 37-40, find the...Ch. 10.1 - Prob. 40ECh. 10.1 - Finding the Standard Equation of a Hyperbola In...Ch. 10.1 - Finding the Standard Equation of a Hyperbola In...Ch. 10.1 - Finding the Standard Equation of a Hyperbola In...Ch. 10.1 - Prob. 44ECh. 10.1 - Finding the Standard Equation of a Hyperbola In...Ch. 10.1 - Finding the Standard Equation of a Hyperbola In...Ch. 10.1 - Finding the Standard Equation of a Hyperbola In...Ch. 10.1 - Finding the Standard Equation of a Hyperbola In...Ch. 10.1 - Finding Equations of Tangent Lines and Normal...Ch. 10.1 - Prob. 50ECh. 10.1 - Classifying the Graph of an Equation In Exercises...Ch. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - Classifying the Graph of an Equation In Exercises...Ch. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Prob. 59ECh. 10.1 - HOW DO YOU SEE IT? Describe in words bow a plane...Ch. 10.1 - Solar Collector A solar collector for heating...Ch. 10.1 - Beam Deflection A simply supported beam that is 16...Ch. 10.1 - Proof (a) Prove that any two distinct tangent...Ch. 10.1 - Prob. 64ECh. 10.1 - Bridge Design A cable of a suspension bridge is...Ch. 10.1 - Prob. 66ECh. 10.1 - Prob. 67ECh. 10.1 - Surface Area A satellite signal receiving dish is...Ch. 10.1 - Orbit of Earth Earth moves in an elliptical orbit...Ch. 10.1 - Satellite Orbit The apogee(the point in orbit...Ch. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Halleys Comet Probably the most famous of all...Ch. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - Prob. 76ECh. 10.1 - Arc Length Use the integration capabilities of a...Ch. 10.1 - Prob. 78ECh. 10.1 - Geometry The area of the ellipse in the figure is...Ch. 10.1 - Proof Prove Theorem 10.4 by showing dial the...Ch. 10.1 - Prob. 81ECh. 10.1 - Hyperbola Consider a hyperbola centered at the...Ch. 10.1 - Navigation LORAN (long distance radio navigation)...Ch. 10.1 - Hyperbolic Mirror A hyperbolic mirror (used in...Ch. 10.1 - Prob. 85ECh. 10.1 - Proof Prove that the graph of the equation...Ch. 10.1 - Prob. 87ECh. 10.1 - Prob. 88ECh. 10.1 - Prob. 89ECh. 10.1 - True or False? In Exercises 87-92, determine...Ch. 10.1 - True or False? In Exercises 8792, determine...Ch. 10.1 - Prob. 92ECh. 10.1 - For a point P on an ellipse, let d be the distance...Ch. 10.1 - Find the minimum value of (uv)2+(2u29v)2 for 0u2...Ch. 10.2 - Parametric Equations What information does a set...Ch. 10.2 - Prob. 2ECh. 10.2 - Think About It How can two sets of parametric...Ch. 10.2 - Adjusting a Domain Consider the parametric...Ch. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Using Parametric Equations In Exercises 5-22,...Ch. 10.2 - Using Parametric Equations In Exercises 5-22,...Ch. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Using Parametric Equations In Exercises 23-34, use...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - Prob. 42ECh. 10.2 - Prob. 43ECh. 10.2 - Writing a Set of Parametric Equations In Exercises...Ch. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Prob. 53ECh. 10.2 - Prob. 54ECh. 10.2 - Prob. 55ECh. 10.2 - Prob. 56ECh. 10.2 - Prob. 57ECh. 10.2 - Prob. 58ECh. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - Prob. 62ECh. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Prob. 66ECh. 10.2 - Prob. 67ECh. 10.2 - Prob. 68ECh. 10.2 - Prob. 69ECh. 10.2 - Prob. 70ECh. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - Prob. 73ECh. 10.2 - Prob. 74ECh. 10.2 - Curtate Cycloid A wheel of radius a rolls along a...Ch. 10.2 - Prob. 76ECh. 10.2 - Prob. 77ECh. 10.2 - True or False? In Exercises 77-79, determine...Ch. 10.2 - Prob. 79ECh. 10.2 - Prob. 80ECh. 10.2 - Projectile Motion In Exercises 81 and 82, consider...Ch. 10.2 - Prob. 82ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Finding a Derivative. In Exercises 58, find dy/dx....Ch. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Finding an Equation of a Tangent Line In Exercises...Ch. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Finding Equations of Tangent Lines In Exercises...Ch. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Determining Concavity In Exercises 43-48,...Ch. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Arc Length In Exercises 49-54, find the arc length...Ch. 10.3 - Prob. 54ECh. 10.3 - Arc Length In Exercises 55-58, find the arc length...Ch. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Prob. 60ECh. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Prob. 67ECh. 10.3 - Prob. 68ECh. 10.3 - Prob. 69ECh. 10.3 - Prob. 70ECh. 10.3 - Prob. 71ECh. 10.3 - Prob. 72ECh. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.3 - Prob. 75ECh. 10.3 - Prob. 76ECh. 10.3 - Prob. 77ECh. 10.3 - Prob. 78ECh. 10.3 - Area In Exercises 79 and 80, find the area of the...Ch. 10.3 - Prob. 80ECh. 10.3 - Prob. 81ECh. 10.3 - Prob. 82ECh. 10.3 - Prob. 83ECh. 10.3 - Prob. 84ECh. 10.3 - Areas of Simple Closed Curves In Exercises 81-86,...Ch. 10.3 - Prob. 86ECh. 10.3 - Prob. 87ECh. 10.3 - Prob. 88ECh. 10.3 - Prob. 89ECh. 10.3 - Prob. 90ECh. 10.3 - Prob. 91ECh. 10.3 - Prob. 92ECh. 10.3 - Involute of a Circle The involute of a circle is...Ch. 10.3 - Prob. 94ECh. 10.3 - Prob. 95ECh. 10.3 - Tractrix A person moves from the origin along the...Ch. 10.3 - Prob. 97ECh. 10.3 - Prob. 98ECh. 10.3 - Prob. 99ECh. 10.3 - Prob. 100ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Rectangular-to-Polar Conversion In Exercises...Ch. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Polar-to-Rectangular Conversion In Exercises...Ch. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Prob. 59ECh. 10.4 - Prob. 60ECh. 10.4 - Prob. 61ECh. 10.4 - Prob. 62ECh. 10.4 - Prob. 63ECh. 10.4 - Prob. 64ECh. 10.4 - Prob. 65ECh. 10.4 - Prob. 66ECh. 10.4 - Prob. 67ECh. 10.4 - Prob. 68ECh. 10.4 - Prob. 69ECh. 10.4 - Prob. 70ECh. 10.4 - Prob. 71ECh. 10.4 - Prob. 72ECh. 10.4 - Prob. 73ECh. 10.4 - Prob. 74ECh. 10.4 - Prob. 75ECh. 10.4 - Prob. 76ECh. 10.4 - Prob. 77ECh. 10.4 - Prob. 78ECh. 10.4 - Prob. 79ECh. 10.4 - Prob. 80ECh. 10.4 - Prob. 81ECh. 10.4 - Prob. 82ECh. 10.4 - Prob. 83ECh. 10.4 - Prob. 84ECh. 10.4 - Prob. 85ECh. 10.4 - Prob. 86ECh. 10.4 - 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Finding the Area of a Polar Region In Exercises...Ch. 10.5 - Finding the Area of a Polar Region In Exercises...Ch. 10.5 - Finding the Area of a Polar Region In Exercises...Ch. 10.5 - Finding the Area of a Polar Region In Exercises...Ch. 10.5 - Finding the Area of a Polar Region In Exercises...Ch. 10.5 - Finding the Area of a Polar Region In Exercises...Ch. 10.5 - Finding the Area of a Polar Region In Exercises...Ch. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Area Sketch the strophoid r=sec2cos,22. Convert...Ch. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10.5 - Prob. 63ECh. 10.5 - Prob. 64ECh. 10.5 - Prob. 65ECh. 10.5 - Prob. 66ECh. 10.5 - Prob. 67ECh. 10.5 - Prob. 68ECh. 10.5 - Prob. 69ECh. 10.5 - Prob. 70ECh. 10.5 - Prob. 71ECh. 10.5 - Prob. 72ECh. 10.5 - Prob. 73ECh. 10.5 - Prob. 74ECh. 10.5 - Surface Area of a Torus Find the surface area of...Ch. 10.5 - Prob. 76ECh. 10.5 - Prob. 77ECh. 10.5 - Prob. 78ECh. 10.5 - Prob. 79ECh. 10.5 - Prob. 80ECh. 10.5 - Prob. 81ECh. 10.5 - Prob. 82ECh. 10.5 - Folium of Descartes A curve called the folium of...Ch. 10.5 - Prob. 84ECh. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - Prob. 33ECh. 10.6 - Prob. 34ECh. 10.6 - Prob. 35ECh. 10.6 - Prob. 36ECh. 10.6 - Prob. 37ECh. 10.6 - Prob. 38ECh. 10.6 - Prob. 39ECh. 10.6 - Prob. 40ECh. 10.6 - Prob. 41ECh. 10.6 - Prob. 42ECh. 10.6 - Prob. 43ECh. 10.6 - Prob. 44ECh. 10.6 - EXPLORING CONCEPTS Eccentricity Consider two...Ch. 10.6 - Prob. 46ECh. 10.6 - Prob. 47ECh. 10.6 - Prob. 48ECh. 10.6 - Prob. 49ECh. 10.6 - Prob. 50ECh. 10.6 - Prob. 51ECh. 10.6 - Prob. 52ECh. 10.6 - Prob. 53ECh. 10.6 - Prob. 54ECh. 10.6 - Prob. 55ECh. 10.6 - Prob. 56ECh. 10.6 - Prob. 57ECh. 10.6 - Prob. 58ECh. 10.6 - Explorer 18 On November 27, 1963, the United...Ch. 10.6 - Prob. 60ECh. 10.6 - Prob. 61ECh. 10.6 - Prob. 62ECh. 10.6 - Prob. 63ECh. 10.6 - Prob. 64ECh. 10.6 - Prob. 65ECh. 10.6 - Comet Hale-Bopp The comet Hale-Bopp has an...Ch. 10.6 - Prob. 67ECh. 10.6 - Eccentricity In Exercises 67 and 68, let r0...Ch. 10 - Matching In Exercises 1-6, match the equation with...Ch. 10 - Matching In Exercises 16, match the equation with...Ch. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Using an Ellipse Consider the ellipse x225+y29=1....Ch. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Serpentine Curve Consider the parametric equations...Ch. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - Prob. 71RECh. 10 - Prob. 72RECh. 10 - Prob. 73RECh. 10 - Prob. 74RECh. 10 - Prob. 75RECh. 10 - Prob. 76RECh. 10 - Prob. 77RECh. 10 - Prob. 78RECh. 10 - Prob. 79RECh. 10 - Prob. 80RECh. 10 - Prob. 81RECh. 10 - Prob. 82RECh. 10 - Prob. 83RECh. 10 - Prob. 84RECh. 10 - Prob. 85RECh. 10 - Prob. 86RECh. 10 - Prob. 87RECh. 10 - 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Arc Length A particle is moving along the path...Ch. 10 - Prob. 13PSCh. 10 - Prob. 14PSCh. 10 - Prob. 15PSCh. 10 - Prob. 16PSCh. 10 - Prob. 17PS
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- 3. Consider the sequences of functions f₁: [-π, π] → R, sin(n²x) An(2) n f pointwise as (i) Find a function ƒ : [-T,π] → R such that fn n∞. Further, show that fn →f uniformly on [-π,π] as n → ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7, 7]? Justify your answer. [10 Marks]arrow_forward1. (i) Give the definition of a metric on a set X. [5 Marks] (ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4, d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer. = (iii) Consider a metric space (R, d.), where = [10 Marks] 0 if x = y, d* (x, y) 5 if xy. In the metric space (R, d*), describe: (a) open ball B2(0) of radius 2 centred at 0; (b) closed ball B5(0) of radius 5 centred at 0; (c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] [5 Marks] [5 Marks]arrow_forward(c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] 2. Let C([a, b]) be the metric space of continuous functions on the interval [a, b] with the metric doo (f,g) = max f(x)g(x)|. xЄ[a,b] = 1x. Find: Let f(x) = 1 - x² and g(x): (i) do(f, g) in C'([0, 1]); (ii) do(f,g) in C([−1, 1]). [20 Marks] [20 Marks]arrow_forward
- Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties to find lim→-4 1 [2h (x) — h(x) + 7 f(x)] : - h(x)+7f(x) 3 O DNEarrow_forward17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t). (a) How much of the slope field can you sketch from this information? [Hint: Note that the differential equation depends only on t.] (b) What can you say about the solu- tion with y(0) = 2? (For example, can you sketch the graph of this so- lution?) y(0) = 1 y ANarrow_forward(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Proarrow_forward
- Evaluate the integral using integration by parts. Sx² cos (9x) dxarrow_forwardLet f be defined as follows. y = f(x) = x² - 5x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4. Need Help? Read It Master Itarrow_forwardVelocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t². (a) What is the average velocity of the ball over the following time intervals? [3,4] [3, 3.5] [3, 3.1] ft/sec ft/sec ft/sec (b) What is the instantaneous velocity at time t = 3? ft/sec (c) What is the instantaneous velocity at time t = 7? ft/sec Is the ball rising or falling at this time? O rising falling (d) When will the ball hit the ground? t = sec Need Help? Read It Watch Itarrow_forward
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