Deck 15: Section 5: Vector Analysis

ملء الشاشة (f)
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سؤال
Identify the surface by eliminating the parameters from the vector-valued function <strong>Identify the surface by eliminating the parameters from the vector-valued function   .</strong> A) plane B) sphere C) paraboloid D) cylinder E) ellipsoid <div style=padding-top: 35px> .

A) plane
B) sphere
C) paraboloid
D) cylinder
E) ellipsoid
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سؤال
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone, <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> where <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> and sketch the graph.

A) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a vector-valued function whose graph is the plane <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere, <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point. <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis. <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Match the following vector-valued function with its graph. <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> about the x-axis.

A) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Match the following vector-valued function with its graph. <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the surface given by <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , where <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the area of the surface of revolution <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a vector-valued function whose graph is the ellipsoid <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a vector-valued function whose graph is the cone <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a vector-valued function whose graph is the part of the paraboloid <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> that lies inside the cylinder <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface. <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
The surface of the dome on a new museum is given by <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> and <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is in meters. Find the surface area of the dome.

A) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a vector-valued function for the hyperboloid <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a vector-valued function whose graph is the cylinder <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine the tangent plane for the hyperboloid <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 15: Section 5: Vector Analysis
1
Identify the surface by eliminating the parameters from the vector-valued function <strong>Identify the surface by eliminating the parameters from the vector-valued function   .</strong> A) plane B) sphere C) paraboloid D) cylinder E) ellipsoid .

A) plane
B) sphere
C) paraboloid
D) cylinder
E) ellipsoid
ellipsoid
2
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone, <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   where <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone,   where   .</strong> A)   B)   C)   D)   E)
3
Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)   and sketch the graph.

A) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)
B) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)
C) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)
D) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)
E) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   and sketch the graph.</strong> A)   B)   C)   D)   E)
4
Find a vector-valued function whose graph is the plane <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)
B) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)
C) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)
D) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)
E) <strong>Find a vector-valued function whose graph is the plane   .</strong> A)   B)   C)   D)   E)
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5
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere, <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)

A) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,  </strong> A)   B)   C)   D)   E)
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6
Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point. <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)

A) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)
B) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)
C) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)
D) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)
E) <strong>Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.  </strong> A)   B)   C)   D)   E)
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7
Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis. <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)

A) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)
B) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)
C) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)
D) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)
E) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.  </strong> A)   B)   C)   D)   E)
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8
Match the following vector-valued function with its graph. <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
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9
Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)   about the x-axis.

A) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)
B) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)
C) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)
D) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)
E) <strong>Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function   about the x-axis.</strong> A)   B)   C)   D)   E)
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10
Match the following vector-valued function with its graph. <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the following vector-valued function with its graph.  </strong> A)   B)   C)   D)   E)
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11
Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function   .</strong> A)   B)   C)   D)   E)
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12
Find the area of the surface given by <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   , where <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface given by   , where   .</strong> A)   B)   C)   D)   E)
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13
Find the area of the surface of revolution <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the area of the surface of revolution   .</strong> A)   B)   C)   D)   E)
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14
Find a vector-valued function whose graph is the ellipsoid <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)
B) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)
C) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)
D) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)
E) <strong>Find a vector-valued function whose graph is the ellipsoid   .</strong> A)   B)   C)   D)   E)
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15
Find a vector-valued function whose graph is the cone <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)
B) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)
C) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)
D) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)
E) <strong>Find a vector-valued function whose graph is the cone   .</strong> A)   B)   C)   D)   E)
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16
Find a vector-valued function whose graph is the part of the paraboloid <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   that lies inside the cylinder <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)
B) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)
C) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)
D) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)
E) <strong>Find a vector-valued function whose graph is the part of the paraboloid   that lies inside the cylinder   .</strong> A)   B)   C)   D)   E)
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17
Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface. <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.  </strong> A)   B)   C)   D)   E)
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18
The surface of the dome on a new museum is given by <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   and <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)   is in meters. Find the surface area of the dome.

A) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)
B) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)
C) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)
D) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)
E) <strong>The surface of the dome on a new museum is given by   and   is in meters. Find the surface area of the dome.</strong> A)   B)   C)   D)   E)
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19
Find a vector-valued function for the hyperboloid <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)
B) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)
C) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)
D) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)
E) <strong>Find a vector-valued function for the hyperboloid   .</strong> A)   B)   C)   D)   E)
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20
Find a vector-valued function whose graph is the cylinder <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)
B) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)
C) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)
D) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)
E) <strong>Find a vector-valued function whose graph is the cylinder   .</strong> A)   B)   C)   D)   E)
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21
Determine the tangent plane for the hyperboloid <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)
B) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)
C) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)
D) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)
E) <strong>Determine the tangent plane for the hyperboloid   .</strong> A)   B)   C)   D)   E)
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