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Exam 14: Calculus of Vector-Valued Functions

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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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A small planet is located eight times as far from the Sun as Earth's distance from the Sun ( A small planet is located eight times as far from the Sun as Earth's distance from the Sun ( m). How many years would it take the planet to orbit the Sun, given that s<sup>2</sup>/m<sup>3</sup>? m). How many years would it take the planet to orbit the Sun, given that A small planet is located eight times as far from the Sun as Earth's distance from the Sun ( m). How many years would it take the planet to orbit the Sun, given that s<sup>2</sup>/m<sup>3</sup>? s2/m3?

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Question 81

Find the point of intersection of the space curves Find the point of intersection of the space curves , and . , and Find the point of intersection of the space curves , and . .

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Question 82

Find the arc length of the curve Find the arc length of the curve . .

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Question 83

Find the domain of the vector-valued function Find the domain of the vector-valued function . .

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Question 84

A satellite has initial position A satellite has initial position and initial velocity (units of kilometers and seconds). Find the equation of the plane containing the satellite's orbit, assuming that the planet is located at the origin. and initial velocity A satellite has initial position and initial velocity (units of kilometers and seconds). Find the equation of the plane containing the satellite's orbit, assuming that the planet is located at the origin. (units of kilometers and seconds). Find the equation of the plane containing the satellite's orbit, assuming that the planet is located at the origin.

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Question 85

A projectile is fired at an angle of A projectile is fired at an angle of and lands 250 meters away. What was its initial speed? Approximate your answer to the nearest tenth meter per second. and lands 250 meters away. What was its initial speed? Approximate your answer to the nearest tenth meter per second.

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Question 86

Suppose an asteroid traverses a circular orbit of radius 10,000 km about a planet of mass Suppose an asteroid traverses a circular orbit of radius 10,000 km about a planet of mass kg. What is the period of the orbit? Recall . kg. What is the period of the orbit? Recall Suppose an asteroid traverses a circular orbit of radius 10,000 km about a planet of mass kg. What is the period of the orbit? Recall . .

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Question 87

The curvature of The curvature of at the point is: at the point The curvature of at the point is: is:

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Question 88

The position of a particle for time The position of a particle for time is given by . Find the speed of the particle when it touches the curve parametrized by . is given by The position of a particle for time is given by . Find the speed of the particle when it touches the curve parametrized by . . Find the speed of the particle when it touches the curve parametrized by The position of a particle for time is given by . Find the speed of the particle when it touches the curve parametrized by . .

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Question 89

Find a point on the curve Find a point on the curve where the tangent line is parallel to the plane . where the tangent line is parallel to the plane Find a point on the curve where the tangent line is parallel to the plane . .

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Question 90

Parameterize the curve of intersection between the sphere Parameterize the curve of intersection between the sphere and the cone and identify the curve. and the cone Parameterize the curve of intersection between the sphere and the cone and identify the curve. and identify the curve.

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Question 91

Evaluate Evaluate for the parametrization for the parametrization Evaluate for the parametrization

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Question 92

Find the unit normal vector Find the unit normal vector , the curvature , and the center of the osculating circle at , for the curve . , the curvature Find the unit normal vector , the curvature , and the center of the osculating circle at , for the curve . , and the center of the osculating circle at Find the unit normal vector , the curvature , and the center of the osculating circle at , for the curve . , for the curve Find the unit normal vector , the curvature , and the center of the osculating circle at , for the curve . .

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Question 93

Evaluate the definite integrals. A) Evaluate the definite integrals. A) B) B) Evaluate the definite integrals. A) B)

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Question 94

Find the unit normal vector to Find the unit normal vector to at . at Find the unit normal vector to at . .

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Question 95

A particle's position at time A particle's position at time is given by . Find at is given by A particle's position at time is given by . Find at . Find A particle's position at time is given by . Find at at A particle's position at time is given by . Find at

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Question 96

For the parametrization For the parametrization , find the curvature of the path at , find the curvature of the path at For the parametrization , find the curvature of the path at

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Question 97

The curvature for The curvature for is: is:

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Question 98

A particle moves along the curve A particle moves along the curve The speed of the particle at is approximately: The speed of the particle at A particle moves along the curve The speed of the particle at is approximately: is approximately:

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