Calculus Answers, Learning Aids & Study Resources

____ 15. Some planet an oblate ellipsoid rather than a

____ 15. Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4961 miles and the polar radius is 4687 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is.

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____ 15. Some planet an oblate ellipsoid rather than a

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____ 16. Find a polar equation for the parabola with

16. Find a polar equation for the parabola with its focus at the pole and vertex . a. b. c. d. e. 17. Find a polar equation for the ellipse with its focus at the pole and vertices . a. b. c. d. e. 18. Find a polar equation.

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____ 16. Find a polar equation for the parabola with

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____ 11. Find the area of the parallelogram with the

11. Find the area of the parallelogram with the vertices . Round your answer to two decimal places. a. 35.00 b. 3.00 c. 5.92 d. 7.00 e. 2.65 12. Find the area of the triangle with the vertices , and . Round your answer to two decimal places. a. 20.00 b. 8.00 c. 6.00 d. 2.24 e. 4.47 13..

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____ 11. Find the area of the parallelogram with the

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12.2 Differentiation and Integration of Vector-Values Functions Multiple Choice Identify

12.2 Differentiation and Integration of Vector-Values Functions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the vectors r(t) and r’(t) for the following vector function. a. b. c. d. e. 2. Find r’(t) given the following vector function. a. b. c. d..

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12.2 Differentiation and Integration of Vector-Values Functions Multiple Choice Identify

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11.6 Surfaces in Space Multiple Choice Identify the choice that

11.6 Surfaces in Space Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the equation of the following graph. a. b. c. d. e. 2. Identify the equation of the following graph. a. b. c. d. e. 3. Identify the following quadric.

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11.6 Surfaces in Space Multiple Choice Identify the choice that

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____ 21. Classify the graph of the equation as a

21. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. a. hyperbola b. circle c. ellipse d. parabola 22. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. a. parabola b. circle c. ellipse d. hyperbola 23. Suppose a church window is bounded.

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____ 21. Classify the graph of the equation as a

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11.7 Cylindrical and Spherical Coordinates Multiple Choice Identify the choice

11.7 Cylindrical and Spherical Coordinates Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Convert the following point from cylindrical coordinates to rectangular coordinates. a. b. c. d. e. 2. Convert the following point from rectangular coordinates to cylindrical coordinates. Give any angles.

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11.7 Cylindrical and Spherical Coordinates Multiple Choice Identify the choice

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11.2 Space Coordinates and Vectors in Space Multiple Choice Identify

11.2 Space Coordinates and Vectors in Space Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the coordinates of the point that is located 4 units behind the yz-plane, 6 units to the left of xz-plane, and 4 units above the xy-plane. a..

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11.2 Space Coordinates and Vectors in Space Multiple Choice Identify

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____ 11. Find the foci of the ellipse given by

11. Find the foci of the ellipse given by . a. b. c. d. e. 12. Find the center, foci, vertices, and eccentricity of the ellipse. a. b. c. d. e. 13. Find the eccentricity of the ellipse given by . a. b. c. d. e. 14. Find the.

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____ 11. Find the foci of the ellipse given by

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____ 11. Find an equation of a plane passing through

____ 11. Find an equation of a plane passing through the given point and perpendicular to the given vector. a. 6x – 5y + 4z – 1 = 0 b. 6x + 5y - 4z + 1 = 0 c. 6x + 5y + 4z – 1 = 0 d. 6x + 5y +.

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____ 11. Find an equation of a plane passing through

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11.4 The Cross Product of Two Vectors in Space Multiple

11.4 The Cross Product of Two Vectors in Space Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the cross product of the unit vector k × i. a. j b. i c. -k d. -j e. k 2. Sketch the graph of the cross product of.

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11.4 The Cross Product of Two Vectors in Space Multiple

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10.2 Plane Curves and Parametric Equations Multiple Choice Identify the choice that

10.2 Plane Curves and Parametric Equations Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the corresponding rectangular equation for the curve represented by the parametric equation by eliminating the parameter. a. b. c. d. e. 2. Sketch the curve represented by the parametric.

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10.2 Plane Curves and Parametric Equations Multiple Choice Identify the choice that

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____ 6. Find the focus of the parabola given by

6. Find the focus of the parabola given by . a. b. c. d. e. 7. Find the directrix of the parabola given by y2 – 44y – 48x = 0. a. x = -123 b. x = -122 c. x = 120 d. x = 121 e. x = 122 8. Find the.

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____ 6. Find the focus of the parabola given by

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____ 6. Find given the following vector function. a. 32

6. Find given the following vector function. a. 32 + 52t b. 16 + 52t c. 32 + 26t d. 16 + 26t e. 32 + 52t2 7. Find given the following vector function. a. cost sint b. -34 cos t sin t c. 34 cos t sin t d. -16 sin t cos t e. 3.

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____ 6. Find given the following vector function. a. 32

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____ 16. To carry a 500-pound cylindrical weight, two workers

____ 16. To carry a 500-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder. One rope makes a angle away from the vertical and the other makes a angle as shown in the figure below. Find.

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____ 16. To carry a 500-pound cylindrical weight, two workers

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12.5 Arc Length and Curvature Multiple Choice Identify the choice

12.5 Arc Length and Curvature Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the plane curve given below. a. 20 b. 9 c. 17 d. 19 e. 18 2. A baseball is hit 5 feet above the ground at 140 feet per second.

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12.5 Arc Length and Curvature Multiple Choice Identify the choice

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____ 6. Find a set of parametric equations of the

6. Find a set of parametric equations of the line that passes through the point (-2, 5, -1) and is parallel to the xy-plane and yz-plane. a. b. c. d. e. 7. Determine whether any of the lines given below are parallel or identical. a. are identical b. are.

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____ 6. Find a set of parametric equations of the

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____ 15. Evaluate the limit given below. a. r(t) = i

15. Evaluate the limit given below. a. r(t) = i + 2j b. r(t) = i c. r(t) = 2j d. r(t) = 0 e. The limitt does not exist. 16. Determine the interval on which the vector-valued function is continuous. a. (9, ?) b. (5, ?) c. [5, ?) d. [9, ?) e. (-5, ?) 17. Suppose.

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____ 15. Evaluate the limit given below. a. r(t) = i

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____ 11. Given the equation of a surface of revolution

11. Given the equation of a surface of revolution x2 + z2 – 3y = 0, find the equation of its generating curve in the yz-plane rotating about the y-axis. a. b. c. d. e. 12. Use the shell method to find the volume of the solid below the.

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____ 11. Given the equation of a surface of revolution

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____ 11. Find the curvature of the plane curve .

11. Find the curvature of the plane curve . Round your answer to three decimal places. a. 0.498 b. 0.332 c. 0.015 d. 0.005 e. 0.003 12. Find the radius of curvature of the plane curve . Round your answer to three decimal places. a. 24.694 b. 85.333 c. 28.133 d. 34.510 e. 37.510 13. Find the point on.

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____ 11. Find the curvature of the plane curve .

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____ 11. Determine the range of a projectile fired at

____ 11. Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer.

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____ 11. Determine the range of a projectile fired at

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____ 11. Find a vector-valued function, using the given parameter,

11. Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. a. b. c. d. e. 12. Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. a. b. c. d. e. 13. Find a.

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____ 11. Find a vector-valued function, using the given parameter,

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____ 16. Find the center, foci, and vertices of the

16. Find the center, foci, and vertices of the hyperbola. a. b. c. d. e. 17. Find an equation of the hyperbola with vertices and asymptotes y = ±2x. a. b. c. d. e. 18. Find an equation of the hyperbola with vertices (0, -5)(0, 5) and asymptotes a..

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____ 16. Find the center, foci, and vertices of the

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____ 11. Given and , find the projection of

11. Given and , find the projection of u onto v. a. b. c. d. e. 12. Given , find the vector component of u orthogonal to v. a. b. c. d. e. 13. Suppose the vector gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively,.

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____ 11. Given and , find the projection of

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____ 11. Given , find . a. b. c. d. e.

11. Given , find . a. b. c. d. e. 12. Given , sketch the graph of 5/2 v. a. b. c. d. e. 13. Find the vector . a. b. c. d. e. 14. Find the magnitude of the vector given below. a. b. c. d. e. 15. Find the unit vector in.

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____ 11. Given , find . a. b. c. d. e.

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____ 16. Find a unit vector u in the direction

16. Find a unit vector u in the direction opposite of . a. b. c. d. e. 17. Find the vector v with the magnitude 15/2 and direction of . a. b. c. d. e. 18. Given the vector v lies in the yz-plane, has magnitude 8, and makes.

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____ 16. Find a unit vector u in the direction

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____ 6. Determine whether u and v orthogonal, parallel and

6. Determine whether u and v are orthogonal, parallel and pointing in the same direction, parallel and pointing in opposite directions, or neither. a. Orthogonal b. Parallel, opposite direction c. Parallel, same direction d. Neither parallel nor orthogonal 7. Determine whether u and v are orthogonal, parallel or neither. a. Parallel, same direction b. Orthogonal c..

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____ 6. Determine whether u and v orthogonal, parallel and

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____ 11. Find an equation in spherical coordinates for the

11. Find an equation in spherical coordinates for the equation given in rectangular coordinates. x2 + y2 – 4z2 = 3 a. b. c. d. e. 12. Find an equation in rectangular coordinates for the equation given in spherical coordinates. Express the coefficients to two decimal places. a. y = 0.20x b..

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____ 11. Find an equation in spherical coordinates for the

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Multiple Choice Identify the choice that best completes the statement

Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the domain of the vector-valued function given below. a. [-?, 4) b. [0, 4] c. [-4, 4] d. (-?, ?) e. [-4, ?) 2. Find the domain of the vector-valued function given below. where a. (-?, ?) b. [-1, 1] c. [-4,.

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Multiple Choice Identify the choice that best completes the statement

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11.3 The Dot Product of Two Vectors Multiple Choice Identify

11.3 The Dot Product of Two Vectors Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given and find u ? v. a. –8 b. –4 c. 4 d. 7 e. –1 2. Given , find u ? u. a. –6 b. 12 c. –8 d. –2 e. 20 3. Given.

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11.3 The Dot Product of Two Vectors Multiple Choice Identify

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____ 6. Find the arc length for over the

6. Find the arc length for over the interval [0, 2]. Round your answer to two decimal places. a. 67.63 b. 73.37 c. 79.40 d. 49.75 e. 62.97 7. Find the length of the space curve given below. a. ?29 b. 3 c. 3?29 d. 6?29 e. 29 8. Find the curvature K of the curve given below. a..

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____ 6. Find the arc length for over the

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Multiple Choice Identify the choice that best completes the statement

Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. a. , which are equivalent b. which are not equivalent c. , which are equivalent d. , which.

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Multiple Choice Identify the choice that best completes the statement

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12.3 Velocity and Acceleration Multiple Choice Identify the choice that

12.3 Velocity and Acceleration Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. The position vector describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point (2,.

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12.3 Velocity and Acceleration Multiple Choice Identify the choice that

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____ 6. Given and , find u × v. a.

6. Given and , find u × v. a. b. c. d. e. 7. Given u = i + 3j and v = -8i + j + k, find u × v. a. 6i – j + 26k b. 3i – j + 24k c. 3i – j + 25k d. 4i.

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____ 6. Given and , find u × v. a.

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____ 11. Find ?T at time for the space

11. Find ?T at time for the space curve . Round your answer to three decimal places. a. 0.062 b. 0.071 c. 0.659 d. 0.000 e. 0.753 12. Find ?N at time for the space curve . a. 16 b. 0 c. 5 d. 25 e. 4 13. Find ?T at time t = 2 for the.

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____ 11. Find ?T at time for the space

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____ 6. The position vector describes the path of

6. The position vector describes the path of an object moving in space. Find the velocity v(t) of the object. a. b. c. d. e. 7. Use the given acceleration function and initial conditions to find the position at time t = 1. a. b. c. d. e. .

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____ 6. The position vector describes the path of

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____ 6. Sketch the curve represented by the parametric equations,

6. Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter. a. b. c. d. e. none of the above 7. Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter. a. b. c. d..

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____ 6. Sketch the curve represented by the parametric equations,

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11.5 Lines and Planes in Space Multiple Choice Identify the

11.5 Lines and Planes in Space Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find a set of parametric equations of the line through the point (-7, 5, 4) parallel to the vector v = ?8, 5, 2?. a. b. c. d. e..

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11.5 Lines and Planes in Space Multiple Choice Identify the

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12.4 Tangent Vectors and Normal Vectors Multiple Choice Identify the

12.4 Tangent Vectors and Normal Vectors Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the unit tangent vector to the curve given below at the specified point. a. b. c. d. e. 2. Find the unit tangent vector to the.

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12.4 Tangent Vectors and Normal Vectors Multiple Choice Identify the

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____ 6. Given and , find 2u + 5v. a.

6. Given and , find 2u + 5v. a. b. c. d. e. 7. The vector v and its initial point is given. Find the terminal point. , initial point (-6, 10) a. (-3, -8) b. (8, -3) c. (3, 8) d. (3, -8) e. (-3, 8) 8. Find the magnitude of the.

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____ 6. Given and , find 2u + 5v. a.

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____ 15. Suppose a 48000-pound truck parked a 10? slope

____ 15. Suppose a 48000-pound truck is parked on a 10? slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place. a. 47,008.8 lb b. 47,426.8 lb c. 47,328.8 lb d. 47,270.8 lb e..

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____ 15. Suppose a 48000-pound truck parked a 10? slope

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____ 6. Find the standard equation of the sphere with

6. Find the standard equation of the sphere with center at (-2, 3, 6) and tangent to the yz-plane. a. b. c. d. e. 7. Complete the square to write the following equation in the standard form for a sphere. a. b. c. d. e. 8. Find the component.

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____ 6. Find the standard equation of the sphere with

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____ 11. Use the properties of the derivative to find

11. Use the properties of the derivative to find given the following vector-valued functions. a. b. c. d. e. 12. Use the properties of the derivative to find given the following vector-valued functions. a. 2 b. 2/t c. 2t d. 5 e. 0 13. Use the properties of the derivative to find.

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____ 11. Use the properties of the derivative to find

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____ 6. The graph below most likely the graph of

6. The graph below is most likely the graph of which of the following equations? a. b. c. d. e. 7. Sketch the curve represented by the vector-valued function and give the orientation of the curve. a. b. c. d. e. 8. Sketch the curve represented by the vector-valued function and give.

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____ 6. The graph below most likely the graph of

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____ 6. Find the principle unit normal vector to the

6. Find the principle unit normal vector to the curve given below at the specified point. a. b. c. d. e. 7. Find ?T at time t = 1 for the plane curve . Round your answer to three decimal places. a. 11.077 b. 7.310 c. 11.797 d. 5.898 e. 5.538 8. Find ?N.

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____ 6. Find the principle unit normal vector to the

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____ 16. Find the distance between the point (2, -2,

16. Find the distance between the point (2, -2, -3) and the plane 2x – 3y + 4z = 8. a. b. c. d. e. 17. Find the distance between the planes given below. a. b. c. d. e. 18. Find the distance between the point (1, 1, 1).

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____ 16. Find the distance between the point (2, -2,

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____ 11. Find a set of parametric equations for the

11. Find a set of parametric equations for the rectangular equation y = 3x - 5. a. b. c. d. e. 12. Find a set of parametric equations for the rectangular equation y = 2x – 3 that satisfies the condition t = 0 at the point (2, 1). a..

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____ 11. Find a set of parametric equations for the

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____ 6. Find an equation in rectangular coordinates for the

6. Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. r = 4z a. b. c. d. e. 7. Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. r2 +z2 = 4 a. x + y + z = 2 b. x2 + y2 +.

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____ 6. Find an equation in rectangular coordinates for the

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____ 6. Identify the following quadric surface. a. elliptic paraboloid b. elliptic

6. Identify the following quadric surface. a. elliptic paraboloid b. elliptic cone c. hyperboloid of two sheets d. hyperboloid of one sheet e. ellipsoid 7. Identify the following quadric surface. a. hyperboloid of one sheet b. elliptic cone c. elliptic paraboloid d. hyperboloid of two sheets e. hyperbolic paraboloid 8. Identify the following quadric surface. a. Elliptic cone b. Hyperboloid of.

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____ 6. Identify the following quadric surface. a. elliptic paraboloid b. elliptic

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____ 11. Find the component form of vector v given

11. Find the component form of vector v given its magnitude is ||v|| = 7 and the angle it makes with the positive x-axis is ? = 120?. a. b. c. d. e. 12. Find the component form of vector u + v given ||u|| = 2 and ||v||.

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____ 11. Find the component form of vector v given

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____ 15. Some planet an oblate ellipsoid rather than a

____ 15. Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4961 miles and the polar radius is 4687 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is.

____ 15. Some planet an oblate ellipsoid rather than a

____ 16. Find a polar equation for the parabola with

____ 16. Find a polar equation for the parabola with its focus at the pole and vertex . a. b. c. d. e. ____ 17. Find a polar equation for the ellipse with its focus at the pole and vertices . a. b. c. d. e. ____ 18. Find a polar equation.

____ 16. Find a polar equation for the parabola with

____ 11. Find the area of the parallelogram with the

____ 11. Find the area of the parallelogram with the

12.2 Differentiation and Integration of Vector-Values Functions Multiple Choice Identify

12.2 Differentiation and Integration of Vector-Values Functions Multiple Choice Identify

11.6 Surfaces in Space Multiple Choice Identify the choice that

11.6 Surfaces in Space Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Identify the equation of the following graph. a. b. c. d. e. ____ 2. Identify the equation of the following graph. a. b. c. d. e. ____ 3. Identify the following quadric.

11.6 Surfaces in Space Multiple Choice Identify the choice that

____ 21. Classify the graph of the equation as a

____ 21. Classify the graph of the equation as a

11.7 Cylindrical and Spherical Coordinates Multiple Choice Identify the choice

11.7 Cylindrical and Spherical Coordinates Multiple Choice Identify the choice

11.2 Space Coordinates and Vectors in Space Multiple Choice Identify

11.2 Space Coordinates and Vectors in Space Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the coordinates of the point that is located 4 units behind the yz-plane, 6 units to the left of xz-plane, and 4 units above the xy-plane. a..

11.2 Space Coordinates and Vectors in Space Multiple Choice Identify

____ 11. Find the foci of the ellipse given by

____ 11. Find the foci of the ellipse given by . a. b. c. d. e. ____ 12. Find the center, foci, vertices, and eccentricity of the ellipse. a. b. c. d. e. ____ 13. Find the eccentricity of the ellipse given by . a. b. c. d. e. ____ 14. Find the.

____ 11. Find the foci of the ellipse given by

____ 11. Find an equation of a plane passing through

____ 11. Find an equation of a plane passing through the given point and perpendicular to the given vector. a. 6x – 5y + 4z – 1 = 0 b. 6x + 5y - 4z + 1 = 0 c. 6x + 5y + 4z – 1 = 0 d. 6x + 5y +.

____ 11. Find an equation of a plane passing through

11.4 The Cross Product of Two Vectors in Space Multiple

11.4 The Cross Product of Two Vectors in Space Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the cross product of the unit vector k × i. a. j b. i c. -k d. -j e. k ____ 2. Sketch the graph of the cross product of.

11.4 The Cross Product of Two Vectors in Space Multiple

10.2 Plane Curves and Parametric Equations Multiple Choice Identify the choice that

10.2 Plane Curves and Parametric Equations Multiple Choice Identify the choice that

____ 6. Find the focus of the parabola given by

____ 6. Find the focus of the parabola given by . a. b. c. d. e. ____ 7. Find the directrix of the parabola given by y2 – 44y – 48x = 0. a. x = -123 b. x = -122 c. x = 120 d. x = 121 e. x = 122 ____ 8. Find the.

____ 6. Find the focus of the parabola given by

____ 6. Find given the following vector function. a. 32

____ 6. Find given the following vector function. a. 32 + 52t b. 16 + 52t c. 32 + 26t d. 16 + 26t e. 32 + 52t2 ____ 7. Find given the following vector function. a. cost sint b. -34 cos t sin t c. 34 cos t sin t d. -16 sin t cos t e. 3.

____ 6. Find given the following vector function. a. 32

____ 16. To carry a 500-pound cylindrical weight, two workers

____ 16. To carry a 500-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder. One rope makes a angle away from the vertical and the other makes a angle as shown in the figure below. Find.

____ 16. To carry a 500-pound cylindrical weight, two workers

12.5 Arc Length and Curvature Multiple Choice Identify the choice

12.5 Arc Length and Curvature Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the length of the plane curve given below. a. 20 b. 9 c. 17 d. 19 e. 18 ____ 2. A baseball is hit 5 feet above the ground at 140 feet per second.

12.5 Arc Length and Curvature Multiple Choice Identify the choice

____ 6. Find a set of parametric equations of the

____ 6. Find a set of parametric equations of the line that passes through the point (-2, 5, -1) and is parallel to the xy-plane and yz-plane. a. b. c. d. e. ____ 7. Determine whether any of the lines given below are parallel or identical. a. are identical b. are.

____ 6. Find a set of parametric equations of the

____ 15. Evaluate the limit given below. a. r(t) = i

____ 15. Evaluate the limit given below. a. r(t) = i + 2j b. r(t) = i c. r(t) = 2j d. r(t) = 0 e. The limitt does not exist. ____ 16. Determine the interval on which the vector-valued function is continuous. a. (9, ?) b. (5, ?) c. [5, ?) d. [9, ?) e. (-5, ?) ____ 17. Suppose.

____ 15. Evaluate the limit given below. a. r(t) = i

____ 11. Given the equation of a surface of revolution

____ 11. Given the equation of a surface of revolution x2 + z2 – 3y = 0, find the equation of its generating curve in the yz-plane rotating about the y-axis. a. b. c. d. e. ____ 12. Use the shell method to find the volume of the solid below the.

____ 11. Given the equation of a surface of revolution

____ 11. Find the curvature of the plane curve .

____ 11. Find the curvature of the plane curve .

____ 11. Determine the range of a projectile fired at

____ 11. Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer.

____ 11. Determine the range of a projectile fired at

____ 11. Find a vector-valued function, using the given parameter,

____ 11. Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. a. b. c. d. e. ____ 12. Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. a. b. c. d. e. ____ 13. Find a.

____ 11. Find a vector-valued function, using the given parameter,

____ 16. Find the center, foci, and vertices of the

____ 16. Find the center, foci, and vertices of the hyperbola. a. b. c. d. e. ____ 17. Find an equation of the hyperbola with vertices and asymptotes y = ±2x. a. b. c. d. e. ____ 18. Find an equation of the hyperbola with vertices (0, -5)(0, 5) and asymptotes a..

____ 16. Find the center, foci, and vertices of the

____ 11. Given and , find the projection of

____ 11. Given and , find the projection of u onto v. a. b. c. d. e. ____ 12. Given , find the vector component of u orthogonal to v. a. b. c. d. e. ____ 13. Suppose the vector gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively,.

____ 11. Given and , find the projection of

____ 11. Given , find . a. b. c. d. e.

____ 11. Given , find . a. b. c. d. e. ____ 12. Given , sketch the graph of 5/2 v. a. b. c. d. e. ____ 13. Find the vector . a. b. c. d. e. ____ 14. Find the magnitude of the vector given below. a. b. c. d. e. ____ 15. Find the unit vector in.

____ 11. Given , find . a. b. c. d. e.

____ 16. Find a unit vector u in the direction

____ 16. Find a unit vector u in the direction opposite of . a. b. c. d. e. ____ 17. Find the vector v with the magnitude 15/2 and direction of . a. b. c. d. e. ____ 18. Given the vector v lies in the yz-plane, has magnitude 8, and makes.

____ 16. Find a unit vector u in the direction

____ 6. Determine whether u and v orthogonal, parallel and

____ 6. Determine whether u and v orthogonal, parallel and

____ 11. Find an equation in spherical coordinates for the

____ 11. Find an equation in spherical coordinates for the

Multiple Choice Identify the choice that best completes the statement

Multiple Choice Identify the choice that best completes the statement

16. Find a polar equation for the parabola with its focus at the pole and vertex . a. b. c. d. e. 17. Find a polar equation for the ellipse with its focus at the pole and vertices . a. b. c. d. e. 18. Find a polar equation.

11.6 Surfaces in Space Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the equation of the following graph. a. b. c. d. e. 2. Identify the equation of the following graph. a. b. c. d. e. 3. Identify the following quadric.

11. Find the foci of the ellipse given by . a. b. c. d. e. 12. Find the center, foci, vertices, and eccentricity of the ellipse. a. b. c. d. e. 13. Find the eccentricity of the ellipse given by . a. b. c. d. e. 14. Find the.

11.4 The Cross Product of Two Vectors in Space Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the cross product of the unit vector k × i. a. j b. i c. -k d. -j e. k 2. Sketch the graph of the cross product of.

6. Find the focus of the parabola given by . a. b. c. d. e. 7. Find the directrix of the parabola given by y2 – 44y – 48x = 0. a. x = -123 b. x = -122 c. x = 120 d. x = 121 e. x = 122 8. Find the.

6. Find given the following vector function. a. 32 + 52t b. 16 + 52t c. 32 + 26t d. 16 + 26t e. 32 + 52t2 7. Find given the following vector function. a. cost sint b. -34 cos t sin t c. 34 cos t sin t d. -16 sin t cos t e. 3.

12.5 Arc Length and Curvature Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the plane curve given below. a. 20 b. 9 c. 17 d. 19 e. 18 2. A baseball is hit 5 feet above the ground at 140 feet per second.

6. Find a set of parametric equations of the line that passes through the point (-2, 5, -1) and is parallel to the xy-plane and yz-plane. a. b. c. d. e. 7. Determine whether any of the lines given below are parallel or identical. a. are identical b. are.

15. Evaluate the limit given below. a. r(t) = i + 2j b. r(t) = i c. r(t) = 2j d. r(t) = 0 e. The limitt does not exist. 16. Determine the interval on which the vector-valued function is continuous. a. (9, ?) b. (5, ?) c. [5, ?) d. [9, ?) e. (-5, ?) 17. Suppose.

11. Given the equation of a surface of revolution x2 + z2 – 3y = 0, find the equation of its generating curve in the yz-plane rotating about the y-axis. a. b. c. d. e. 12. Use the shell method to find the volume of the solid below the.

11. Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. a. b. c. d. e. 12. Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. a. b. c. d. e. 13. Find a.

16. Find the center, foci, and vertices of the hyperbola. a. b. c. d. e. 17. Find an equation of the hyperbola with vertices and asymptotes y = ±2x. a. b. c. d. e. 18. Find an equation of the hyperbola with vertices (0, -5)(0, 5) and asymptotes a..

11. Given and , find the projection of u onto v. a. b. c. d. e. 12. Given , find the vector component of u orthogonal to v. a. b. c. d. e. 13. Suppose the vector gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively,.

11. Given , find . a. b. c. d. e. 12. Given , sketch the graph of 5/2 v. a. b. c. d. e. 13. Find the vector . a. b. c. d. e. 14. Find the magnitude of the vector given below. a. b. c. d. e. 15. Find the unit vector in.

16. Find a unit vector u in the direction opposite of . a. b. c. d. e. 17. Find the vector v with the magnitude 15/2 and direction of . a. b. c. d. e. 18. Given the vector v lies in the yz-plane, has magnitude 8, and makes.

11.3 The Dot Product of Two Vectors Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given and find u ? v. a. –8 b. –4 c. 4 d. 7 e. –1 2. Given , find u ? u. a. –6 b. 12 c. –8 d. –2 e. 20 3. Given.

6. Find the arc length for over the interval [0, 2]. Round your answer to two decimal places. a. 67.63 b. 73.37 c. 79.40 d. 49.75 e. 62.97 7. Find the length of the space curve given below. a. ?29 b. 3 c. 3?29 d. 6?29 e. 29 8. Find the curvature K of the curve given below. a..

6. Given and , find u × v. a. b. c. d. e. 7. Given u = i + 3j and v = -8i + j + k, find u × v. a. 6i – j + 26k b. 3i – j + 24k c. 3i – j + 25k d. 4i.

11. Find ?T at time for the space curve . Round your answer to three decimal places. a. 0.062 b. 0.071 c. 0.659 d. 0.000 e. 0.753 12. Find ?N at time for the space curve . a. 16 b. 0 c. 5 d. 25 e. 4 13. Find ?T at time t = 2 for the.

6. The position vector describes the path of an object moving in space. Find the velocity v(t) of the object. a. b. c. d. e. 7. Use the given acceleration function and initial conditions to find the position at time t = 1. a. b. c. d. e. .

12.4 Tangent Vectors and Normal Vectors Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the unit tangent vector to the curve given below at the specified point. a. b. c. d. e. 2. Find the unit tangent vector to the.

6. Given and , find 2u + 5v. a. b. c. d. e. 7. The vector v and its initial point is given. Find the terminal point. , initial point (-6, 10) a. (-3, -8) b. (8, -3) c. (3, 8) d. (3, -8) e. (-3, 8) 8. Find the magnitude of the.

6. Find the standard equation of the sphere with center at (-2, 3, 6) and tangent to the yz-plane. a. b. c. d. e. 7. Complete the square to write the following equation in the standard form for a sphere. a. b. c. d. e. 8. Find the component.

11. Use the properties of the derivative to find given the following vector-valued functions. a. b. c. d. e. 12. Use the properties of the derivative to find given the following vector-valued functions. a. 2 b. 2/t c. 2t d. 5 e. 0 13. Use the properties of the derivative to find.

6. The graph below is most likely the graph of which of the following equations? a. b. c. d. e. 7. Sketch the curve represented by the vector-valued function and give the orientation of the curve. a. b. c. d. e. 8. Sketch the curve represented by the vector-valued function and give.

6. Find the principle unit normal vector to the curve given below at the specified point. a. b. c. d. e. 7. Find ?T at time t = 1 for the plane curve . Round your answer to three decimal places. a. 11.077 b. 7.310 c. 11.797 d. 5.898 e. 5.538 8. Find ?N.

16. Find the distance between the point (2, -2, -3) and the plane 2x – 3y + 4z = 8. a. b. c. d. e. 17. Find the distance between the planes given below. a. b. c. d. e. 18. Find the distance between the point (1, 1, 1).

11. Find a set of parametric equations for the rectangular equation y = 3x - 5. a. b. c. d. e. 12. Find a set of parametric equations for the rectangular equation y = 2x – 3 that satisfies the condition t = 0 at the point (2, 1). a..

6. Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. r = 4z a. b. c. d. e. 7. Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. r2 +z2 = 4 a. x + y + z = 2 b. x2 + y2 +.