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Exam 12: Parametric Equations, Polar Coordinates, and Conic Sections

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Exam 1: Precalculus Review74 Questionsadd course
Exam 2: Limits97 Questionsadd course
Exam 3: Differentiation81 Questionsadd course
Exam 4: Applications of the Derivative77 Questionsadd course
Exam 5: The Integral82 Questionsadd course
Exam 6: Applications of the Integral80 Questionsadd course
Exam 7: Exponential Functions106 Questionsadd course
Exam 8: Techniques of Integration101 Questionsadd course
Exam 9: Further Applications of the Integral and Taylor Polynomials100 Questionsadd course
Exam 10: Introduction to Differential Equations73 Questionsadd course
Exam 11: Infinite Series95 Questionsadd course
Exam 12: Parametric Equations, Polar Coordinates, and Conic Sections71 Questionsadd course
Exam 13: Vector Geometry96 Questionsadd course
Exam 14: Calculus of Vector-Valued Functions99 Questionsadd course
Exam 15: Differentiation in Several Variables95 Questionsadd course
Exam 16: Multiple Integration98 Questionsadd course
Exam 17: Line and Surface Integrals92 Questionsadd course
Exam 18: Fundamental Theorems of Vector Analysis91 Questionsadd course
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Find a parametrization for the curve Find a parametrization for the curve from to . from Find a parametrization for the curve from to . to Find a parametrization for the curve from to . .

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Question 61

Find the speed and arc length of Find the speed and arc length of , . , Find the speed and arc length of , . .

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Question 62

Convert the equation Convert the equation to polar coordinates. to polar coordinates.

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Question 63

Find the arc length of the loop of the curve given by the parametric equations Find the arc length of the loop of the curve given by the parametric equations . . Find the arc length of the loop of the curve given by the parametric equations .

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Question 64

The part of the parabola The part of the parabola has a length of . Find the focus and directrix of the parabola. Use . has a length of The part of the parabola has a length of . Find the focus and directrix of the parabola. Use . . Find the focus and directrix of the parabola. Use The part of the parabola has a length of . Find the focus and directrix of the parabola. Use . .

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Question 65

Write the standard equation for the ellipse with foci at Write the standard equation for the ellipse with foci at and , and vertices at and . and Write the standard equation for the ellipse with foci at and , and vertices at and . , and vertices at Write the standard equation for the ellipse with foci at and , and vertices at and . and Write the standard equation for the ellipse with foci at and , and vertices at and . .

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Question 66

Consider the limaçon Consider the limaçon . A) Express as functions of , and find and . B) Find the slopes of the tangent lines to the inner loop of the limaçon at the origin. . Consider the limaçon . A) Express as functions of , and find and . B) Find the slopes of the tangent lines to the inner loop of the limaçon at the origin. A) Express Consider the limaçon . A) Express as functions of , and find and . B) Find the slopes of the tangent lines to the inner loop of the limaçon at the origin. as functions of Consider the limaçon . A) Express as functions of , and find and . B) Find the slopes of the tangent lines to the inner loop of the limaçon at the origin. , and find Consider the limaçon . A) Express as functions of , and find and . B) Find the slopes of the tangent lines to the inner loop of the limaçon at the origin. and Consider the limaçon . A) Express as functions of , and find and . B) Find the slopes of the tangent lines to the inner loop of the limaçon at the origin. . B) Find the slopes of the tangent lines to the inner loop of the limaçon at the origin.

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Question 67

The exact value of the area that lies inside The exact value of the area that lies inside and outside is approximately which of the following? and outside The exact value of the area that lies inside and outside is approximately which of the following? is approximately which of the following? The exact value of the area that lies inside and outside is approximately which of the following?

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Question 68

Write the equation of Write the equation of in Cartesian coordinates. in Cartesian coordinates.

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Question 69

Find the area of the surface generated by revolving the curve Find the area of the surface generated by revolving the curve about the x-axis. about the x-axis.

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Question 70

Calculate the area under the parametrized curve given by Calculate the area under the parametrized curve given by for . for Calculate the area under the parametrized curve given by for . .

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