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Study Resources (Calculus)

  6.Use a double integral to find the volume of the indicated solid.   a. b. c. d. e.   7.Use a double integral to find the volume of the indicated solid.   a. b. c. d. e. none of the above   8.Use a double integral to find the volume of the indicated solid.   a. 16 b. 9 c. 4 d. 20 e. 6   9.Set up and evaluate a double integral to find the volume of the solid.
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  6.Evaluate the following iterated integral.   a. 5,901 b. 5,931 c. 5,955 d. 5,970 e. 6,017   7.Evaluate the following iterated integral.   a. b. c. d. e.   8.Evaluate the following improper integral.   a. b. c. d. e. The integral does not converge.   9.Evaluate the improper iterated integral .   a. b. c. d. e.   10.Use an iterated integral to find the area of the region shown in the figure below. a. b. c. d. e.     .
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MULTIPLE CHOICE 1.Find the area of the portion of the surface that lies above the triangular region with vertices , and .   a. 4 b. 36 c. 18 d. 162 e. 324   2.Find the area of the surface given by over the region R. R: square with vertices   a. b. c. d. e.   3.Find the area of the portion of the surface that lies above.
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  11.Use an iterated integral to find the area of the region bounded by .   a. b. c. d. e. The integral is improper and does not converge.   12.Use an iterated integral to find the area of the region bounded by .   a. b. c. d. e.   13.Use an iterated integral to find the area of the region bounded by the graphs of the equations .
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MULTIPLE CHOICE 1.Find the Jacobian for the following change of variables:   a. b. c. d. e.   2.Find the Jacobian for the change of variables given below.   a. b. c. d. e.   3.Find the Jacobian for the indicated change of variables.   a. b. c. d. e.   4.Find the Jacobian for the following change of variables:   a. b. c. d. e.   5.Find the Jacobian for the following change of variables:   a. b. c. d. e.     .
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MULTIPLE CHOICE 1.Evaluate the following iterated integral.   a. b. c. d. e.   2.Evaluate the following iterated integral.   a. b. c. d. e.   3.Evaluate the iterated integral .   a. b. c. d. e.   4.Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below.   a. b. c. d. e.   5.Set up a triple integral for the volume of the solid bounded by and .   a. b. c. d. e.     .
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  6.Find the gradient of the function at the given point.   a. b. c. d. e.     7.Find the gradient of the function at the given point.   a. b. c. d. e.     8.Find the gradient of the function at the given point.   a. b. c. d. e.     9.Use the gradient to find the directional derivative of the function at P in the direction of Q.   a. b. c. d. e.     10.Use the gradient to find the.
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  16.Use spherical coordinates to find the mass of the sphere with the given density. The density at any point is proportional to the distance of the point from the z-axis.   a. b. c. d. e.   17.Use spherical coordinates to find the z coordinate of the center of mass of the solid lying between two concentric.
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  11.Use cylindrical coordinates to find the volume of the cone where and .   a. b. c. d. e.   12.Use spherical coordinates to find the volume of the solid inside and outside , and above the xy-plane.   a. b. c. d. e.   13.Use spherical coordinates to find the volume of the solid inside the torus given by .   a. b. c. d. e.   14.Use spherical coordinates.
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MULTIPLE CHOICE 1.For the function given by describe the level surface given by .   a. sphere of radius 4 centered at the origin b. circle of radius 4 centered at the origin c. elliptic cone centered at the origin d. sphere of radius 16 centered at the origin e. right circular cone centered at the origin   2.Find the unit normal vector.
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  6.Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformation. a. d. b. e. c.   7.Use the indicated change of variables to evaluate the following double integral.   a. b. c. d. e.     8.Use the indicated change of variables to evaluate the following double integral.   a. b. c. d.   e.   9.Use the following change of variables to evaluate the double integral.
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  11.Given use polar coordinates to set up and evaluate the double integral .   a. b. c. d. e.   12.Use a double integral in polar coordinates to find the volume of the solid in the first octant bounded by the graphs of the equations given below.   a. b. c. d. e.   13.Use a double integral in polar coordinates to find the volume.
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MULTIPLE CHOICE 1.Evaluate the following iterated integral.   a. b. c. d. e.   2.Evaluate the following iterated integral.   a. b. c. d. e.   3.Evaluate the iterated integral .   a. b. c. d. e.   4.Evaluate the following iterated integral.   a. b. c. d. e.   5.Convert the integral below from rectangular coordinates to both cylindrical and spherical coordinates, and evaluate the simpler iterated integral.   a. b. c. d. e.     .
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  6.Set up a triple integral for the volume of the solid bounded above by the cylinder and below by the paraboloid .   a. b. c. d. e.   7.Use a triple integral to find the volume of the solid shown below.   a. b. c. d. e.   8.Use a triple integral to find the volume of the solid shown below.   a. b. c. d. e.   9.Use a triple integral.
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MULTIPLE CHOICE 1.Identify any extrema of the function by recognizing its given form or its form after completing the square.   a. relative maximum: b. relative maximum: c. relative minimum: d. relative minimum: e. relative maximum:   2.Identify any extrema of the function by recognizing its given form or its form after completing the square.   a. relative maximum: b. relative minimum:.
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  11.Determine whether the vector field is conservative. If it is, find a potential function for the vector field.   a. conservative with potential function b. conservative with potential function c. conservative with potential function d. conservative with potential function e. not conservative   12.Find the curl for the vector field at the given point.   a. b. c. d. e.   13.Determine whether the vector field is.
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  6.Evaluate the following iterated integral by converting to polar coordinates.   a. b. c. d. e.   7.Evaluate the iterated integral by converting to polar coordinates.   a. b. c. d. e.   8.Evaluate the following iterated integral by converting to polar coordinates.   a. b. c. d. e.   9.Evaluate the iterated integral by converting to polar coordinates. Round your answer to four decimal places.   a. 10.5742 b. 13.5742 c. 17.5742 d. 28.5742 e. 14.5742   10.Combine the sum of the two iterated.
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  11.Find an equation of the tangent plane to the surface at the point .   a. b. c. d. e.   12.Find symmetric equations of the normal line to the surface at the point .   a. b. c. d. e.   13.Find symmetric equations of the normal line to the surface at the point .   a. b. c. d. e.   14.Find symmetric equations of the normal line to.
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  6.Convert the integral below from rectangular coordinates to both cylindrical and spherical coordinates, and evaluate the simpler iterated integral.   a. b. c. d. e.   7.Use cylindrical coordinates to find the volume of the solid inside both and .   a. b. c. d. e.   8.Use cylindrical coordinates to find the volume of the solid bounded above by and below by .   a. b. c. d. e.   9.Use.
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MULTIPLE CHOICE 1.Match the vector field with its graph   a. c. b. d.   2.Match the vector field with its graph.   a. d. b. e. c.   3.Sketch the vector field .   a. d. b. e. c.   4.Sketch several representative vectors in the vector field given by .   a. d. b. e. c.   5.Compute for the vector field given by .   a. b. c. d. e.     .
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  6.Find the mass of the triangular lamina with vertices for the density .   a. 139,968k b. 279,946k c. 139,958k d. 139,973k e. 279,936k   7.Find the mass of the lamina bounded by the graphs of the equations for the density .   a. b. c. d. e.   8.Find the center of mass of the lamina bounded by the graphs of the equations for the density .   a. b. c. d. e.   9.Find.
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  16.Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the point .   a. b. c. d. e.   17.Consider the two surfaces . Find the cosine of the angle between the gradient vectors at the point . Round your answer to one decimal place.   a. 0.5 b. 0.2 c. 0.1 d. 1.0 e. 0.0   18.Find the angle of inclination .
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  11.Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations and in the first octant.   a. 5,184 b. 576 c. 3,456 d. 1,728 e. 1,152   12.Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below.   a. b. c. d. e.   13.Find.
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MULTIPLE CHOICE 1.Use polar coordinates to describe the region as shown in the figure below:   a. b. c. d. e.   2.Evaluate the double integral below.   a. b. c. d. e.   3.Evaluate the double integral below.   a. b. c. d. e.   4.Identify the region of integration for the following integral.   a. d. b. e. c.   5.Evaluate the double integral below.   a. b. c. d. e.     .
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  11.Sketch the solid whose volume is given by the iterated integral given below and use the sketch to rewrite the integral using the indicated order of integration. Rewrite the integral using the order .   a. b. c. d. e.   12.Find of the center of mass of the solid of given density bounded by the graphs.
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MULTIPLE CHOICE 1.Find the mass of the lamina described by the inequalities given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)   a. 768 b. 128 c. 512 d. 256 e. 392   2.Find the mass of the lamina described by the inequalities given that its density is . (Hint: Some of the integrals are.
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  6.Examine the function for relative extrema.   a. relative minimum: b. relative minimum: c. relative maximum: d. relative maximum: e. no relative extrema   7.Examine the function for relative extrema and saddle points.   a. saddle point: b. relative minimum: c. relative minimum: d. saddle point: e. saddle point:   8. Examine the function for relative extrema and saddle points.   a. relative minimum: b. relative minimum: c. relative maximum: d. saddle point: e. saddle point:   9.Examine the function for.
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MULTIPLE CHOICE 1.Find the minimum distance from the point to the plane . a. b. c. d. e.   2.Find the minimum distance from the point to the surface .   a. b. c. d. e.   3.Find three positive numbers x, y, and z whose sum is 24 and product is a maximum.   a. b. c. d. e.   4.Find three positive numbers x, y, and z whose sum is.
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MULTIPLE CHOICE 1.Evaluate .   a. 3 b. 8 c. 6 d. 9 e. 5   2.Evaluate . Round your answer to two decimal places.   a. 508.64 b. 307.25 c. 2457.99 d. 2224.97 e. 741.66   3.Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R.   a. b. c. d. e.   4.Set up an integral for both orders of integration, and use the more convenient order to evaluate.
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  11.Find the maximum value of the directional derivative at the point of the function . Round your answer to two decimal places.   a. 0.55 b. 0.14 c. 0.56 d. 0.10 e. 0.06     12.Find the maximum value of the directional derivative at the point of the function . Round your answer to two decimal places.   a. 899.28 b. 814.59 c. 922.05 d. 933.23 e. 538.80     13.Find for function .   a. b. c. d. e.     14.For function.
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  11.Find the least squares regression line for the points shown in the graph. a. b. c. d. e.   12. The least squares regression line for the points shown in the graph is . Calculate S, the sum of the squared errors.   a.   b.   c.   d.   e.     13.Find the least squares regression line for the points .   a. b. c. d. e.   14.Find the least squares regression line for.
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  6.Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)   a. b. c. d. e.   7.Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)   a. b. c. d. e.   8.Find the conservative vector field for the potential function by finding its gradient.   a. b. c. d. e.   9.Determine.
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  11.Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function at the critical point , if .   a. relative maximum b. relative minimum c. saddle point d. insufficient information   12.List the critical points of the function for which the Second Partial Test fails.   a. Test fails at.
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MULTIPLE CHOICE 1.Evaluate the following integral.   a. b. c. d. e.   2.Evaluate the following integral.   a. b. c. d. e.   3.Evaluate the following integral.   a. b. c. d. e.   4.Evaluate the following iterated integral.   a. 41.5 b. 38.5 c. 34.5 d. 33.5 e. 37.5   5.Evaluate the following iterated integral.   a. b. c. d. e.     .
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