Calculus Volume 3
Calculus Volume 3
16th Edition
ISBN: 9781938168079
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax
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Vertices Of An Ellipse
In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…
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Chapter 1, Problem 347RE

Determine the Cartesian equation describing the orbit of Pluto, the most eccentric orbit around the Sun. The length of the major axis is 39.26   AU and miner axis is 38 .07   AU . What is the eccentricity?

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The position of a planet that a closest to and farthest from the sun are called its perihelion and aphelion respectively. We know that the Earth orbits around the Sun (as one focus) in an elliptical orbit with the perihelion distance of 1.47 x 108 km and the aphelion distance of 1.52 x 108 km. Find the Cartesian equation of the elliptical orbit.
The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee and perigee of the earth.
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Chapter 1 Solutions

Calculus Volume 3

Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Many plane curves in mathematics are named after...Ch. 1.1 - Earlier in this section, we looked at the...
Ch. 1.1 - Earlier in this section, we looked at the...Ch. 1.1 - Earlier in this section, we looked at the...Ch. 1.1 - Earlier in this section, we looked at the...Ch. 1.1 - Earlier in this section, we looked at the...Ch. 1.1 - For the following exercises, sketch the curves...Ch. 1.1 - For the following exercises, sketch the curves...Ch. 1.1 - For the following exercises, sketch the curves...Ch. 1.1 - For the following exercises, sketch the curves...Ch. 1.1 - For the following exercises, eliminate the...Ch. 1.1 - For the following exercises, use technology (CAS...Ch. 1.1 - For the following exercises, use technology (CAS...Ch. 1.1 - For the following exercises, use technology (CAS...Ch. 1.1 - For the following exercises, use technology (CAS...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, sketch the parametric...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, convert the...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - For the following exercises, the pairs of...Ch. 1.1 - Show that x=h+rcos , y=k+rsin represents the...Ch. 1.1 - Use the equations in the preceding problem to find...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.2 - For the following exercises, each set of...Ch. 1.2 - For the following exercises, each set of...Ch. 1.2 - For the following exercises, each set of...Ch. 1.2 - For the following exercises, each set of...Ch. 1.2 - For the following exercises, determine the slope...Ch. 1.2 - For the following exercises, determine the slope...Ch. 1.2 - For the following exercises, determine the slope...Ch. 1.2 - For the following exercises, determine the slope...Ch. 1.2 - For the following exercises, determine the slope...Ch. 1.2 - For the following exercises, find all points on...Ch. 1.2 - For the following exercises, find all points on...Ch. 1.2 - For the following exercises, find all points on...Ch. 1.2 - For the following exercises, find all points on...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises. find d2y/dx2 . 88....Ch. 1.2 - For the following exercises. find d2y/dx2 . 89....Ch. 1.2 - For the following exercises. find d2y/dx2 . 90....Ch. 1.2 - For the following exercises, find points on the...Ch. 1.2 - For the following exercises, find points on the...Ch. 1.2 - For the following exercises, find dy/dx at the...Ch. 1.2 - For the following exercises, find dy/dx at the...Ch. 1.2 - For the following exercises, find dy/dx at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find d2y/dx2 at the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the arc length...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.2 - For the following exercises, find the area of the...Ch. 1.3 - In the following exercises. plot the point whose...Ch. 1.3 - In the following exercises. plot the point whose...Ch. 1.3 - In the following exercises. plot the point whose...Ch. 1.3 - In the following exercises. plot the point whose...Ch. 1.3 - In the following exercises. plot the point whose...Ch. 1.3 - In the following exercises. plot the point whose...Ch. 1.3 - In the following exercises. plot the point whose...Ch. 1.3 - For the following exercises, consider the polar...Ch. 1.3 - For the following exercises, consider the polar...Ch. 1.3 - For the following exercises, consider the polar...Ch. 1.3 - For the following exercises, consider the polar...Ch. 1.3 - For the following exercises, the rectangular...Ch. 1.3 - For the following exercises, the rectangular...Ch. 1.3 - For the following exercises, the rectangular...Ch. 1.3 - For the following exercises, the rectangular...Ch. 1.3 - For the following exercises, the rectangular...Ch. 1.3 - For the following exercises, the rectangular...Ch. 1.3 - For the following Exercises, find rectangular...Ch. 1.3 - For the following Exercises, find rectangular...Ch. 1.3 - For the following Exercises, find rectangular...Ch. 1.3 - For the following Exercises, find rectangular...Ch. 1.3 - For the following Exercises, find rectangular...Ch. 1.3 - For the following Exercises, find rectangular...Ch. 1.3 - For the following Exercises, find rectangular...Ch. 1.3 - For the following exercises, determine whether the...Ch. 1.3 - For the following exercises, determine whether the...Ch. 1.3 - For the following exercises, determine whether the...Ch. 1.3 - For the following exercises, determine whether the...Ch. 1.3 - For the following exercises, determine whether the...Ch. 1.3 - For the following exercises, describe the graph of...Ch. 1.3 - For the following exercises, describe the graph of...Ch. 1.3 - For the following exercises, describe the graph of...Ch. 1.3 - For the following exercises, describe the graph of...Ch. 1.3 - For the following exercises, convert the...Ch. 1.3 - For the following exercises, convert the...Ch. 1.3 - For the following exercises, convert the...Ch. 1.3 - For the following exercises, convert the...Ch. 1.3 - For the following exercises, convert the...Ch. 1.3 - For the following exercises, convert the polar...Ch. 1.3 - For the following exercises, convert the polar...Ch. 1.3 - For the following exercises, convert the polar...Ch. 1.3 - For the following exercises, convert the polar...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - For the following exercises, sketch a graph of the...Ch. 1.3 - [T] The graph of r=2cos(2)sec() . is called a...Ch. 1.3 - [T] Use a graphing utility and sketch the graph of...Ch. 1.3 - [T] Use a graphing utility to graph r=11cos.Ch. 1.3 - [T] Use technology to graph r=esin()2cos(4) .Ch. 1.3 - [T] Use technology to plot r=sin(37) (use the...Ch. 1.3 - Without using technology, sketch the polar curve...Ch. 1.3 - [T] Use a graphing utility to plot r=sin forCh. 1.3 - [T] Use technology to plot r=e0.1 for 1010 .Ch. 1.3 - [T] There is a curve known as the “Black Hole”....Ch. 1.3 - [T] Use the results of the preceding two problems...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, determine a definite...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find the area of the...Ch. 1.4 - For the following exercises, find a definite...Ch. 1.4 - For the following exercises, find a definite...Ch. 1.4 - For the following exercises, find a definite...Ch. 1.4 - For the following exercises, find a definite...Ch. 1.4 - For the following exercises, find the length of...Ch. 1.4 - For the following exercises, find the length of...Ch. 1.4 - For the following exercises, find the length of...Ch. 1.4 - For the following exercises, find the length of...Ch. 1.4 - For the following exercises, find the length of...Ch. 1.4 - For the following exercises, use the integration...Ch. 1.4 - For the following exercises, use the integration...Ch. 1.4 - For the following exercises, use the integration...Ch. 1.4 - For the following exercises, use the integration...Ch. 1.4 - For the following exercises, use the integration...Ch. 1.4 - For the following exercises, use the familiar...Ch. 1.4 - For the following exercises, use the familiar...Ch. 1.4 - For the following exercises, use the familiar...Ch. 1.4 - For the following exercises, use the familiar...Ch. 1.4 - For the following exercises, use the familiar...Ch. 1.4 - For the following exercises, use the familiar...Ch. 1.4 - For the following exercises, use the familiar...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - For the following exercises, find the slope of a...Ch. 1.4 - Find the points on the interval at which the...Ch. 1.4 - For the cardioid r=1+sin , find the slope of the...Ch. 1.4 - For the following exercises, find the slope of the...Ch. 1.4 - For the following exercises, find the slope of the...Ch. 1.4 - For the following exercises, find the slope of the...Ch. 1.4 - For the following exercises, find the slope of the...Ch. 1.4 - For the following Exercises, find the points at...Ch. 1.4 - For the following Exercises, find the points at...Ch. 1.4 - For the following Exercises, find the points at...Ch. 1.4 - For the following Exercises, find the points at...Ch. 1.4 - For the following Exercises, find the points at...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following Exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, determine the...Ch. 1.5 - For the following exercises, consider the...Ch. 1.5 - For the following exercises, consider the...Ch. 1.5 - For the following exercises, consider the...Ch. 1.5 - For the following exercises, consider the...Ch. 1.5 - For the following exercises, consider the...Ch. 1.5 - For the following exercises, consider the...Ch. 1.5 - For the following exercises, find a polar equation...Ch. 1.5 - For the following exercises, find a polar equation...Ch. 1.5 - For the following exercises, find a polar equation...Ch. 1.5 - For the following exercises, find a polar equation...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following equations, determine which of...Ch. 1.5 - For the following equations, determine which of...Ch. 1.5 - For the following equations, determine which of...Ch. 1.5 - For the following equations, determine which of...Ch. 1.5 - For the following equations, determine which of...Ch. 1.5 - For the following equations, determine which of...Ch. 1.5 - The mirror in an automobile headlight has a...Ch. 1.5 - A satellite dish is shaped like a paraboloid of...Ch. 1.5 - Consider the satellite dish of the preceding...Ch. 1.5 - A searchlight is shaped like a paraboloid of...Ch. 1.5 - Whispering galleries are rooms designed with...Ch. 1.5 - A person is standing 8feet from the nearest wall...Ch. 1.5 - For the following exercises, determine the polar...Ch. 1.5 - For the following exercises, determine the polar...Ch. 1.5 - For the following exercises, determine the polar...Ch. 1.5 - For the following exercises, determine the polar...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - For the following exercises, sketch the parametric...Ch. 1 - For the following exercises, sketch the parametric...Ch. 1 - For the following exercises, sketch the parametric...Ch. 1 - For the following exercises, sketch the parametric...Ch. 1 - For the following exercises, sketch the polar...Ch. 1 - For the following exercises, sketch the polar...Ch. 1 - For the following exercises, find the polar...Ch. 1 - For the following exercises, find the polar...Ch. 1 - For the following exercises, find the equation of...Ch. 1 - For the following exercises, find the equation of...Ch. 1 - For the following exercises, find the equation of...Ch. 1 - For the following exercises, find the area of the...Ch. 1 - For the following exercises, find the area of the...Ch. 1 - For the following exercises, find the arc length...Ch. 1 - For the following exercises, find the arc length...Ch. 1 - For the following exercises, find the Cartesian...Ch. 1 - For the following exercises, find the Cartesian...Ch. 1 - For the following exercises, find the Cartesian...Ch. 1 - For the following exercises, determine the...Ch. 1 - For the following exercises, determine the...Ch. 1 - For the following exercises, determine the...Ch. 1 - Determine the Cartesian equation describing the...Ch. 1 - The C/1980E1 comet was observed in 1980 . Given an...

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Calculus Volume 1

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