Deck 13: Extension F: Vector Calculus

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Question
Find an equation of the tangent plane to the parametric surface represented by r at the specified point. Find an equation of the tangent plane to the parametric surface represented by r at the specified point.   ;  <div style=padding-top: 35px> ; Find an equation of the tangent plane to the parametric surface represented by r at the specified point.   ;  <div style=padding-top: 35px>
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Question
Set up,but do not evaluate,a double integral for the area of the surface with parametric equations Set up,but do not evaluate,a double integral for the area of the surface with parametric equations  <div style=padding-top: 35px>
Question
Match the equation with one of the graphs below. <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
Question
Find the area of the surface S where S is the part of the surface Find the area of the surface S where S is the part of the surface   that lies inside the cylinder  <div style=padding-top: 35px> that lies inside the cylinder Find the area of the surface S where S is the part of the surface   that lies inside the cylinder  <div style=padding-top: 35px>
Question
Find the area of the surface S where S is the part of the plane Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and   <div style=padding-top: 35px> that lies above the triangular region with vertices Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and   <div style=padding-top: 35px> Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and   <div style=padding-top: 35px> ,and Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and   <div style=padding-top: 35px>
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Deck 13: Extension F: Vector Calculus
1
Find an equation of the tangent plane to the parametric surface represented by r at the specified point. Find an equation of the tangent plane to the parametric surface represented by r at the specified point.   ;  ; Find an equation of the tangent plane to the parametric surface represented by r at the specified point.   ;
Answers may vary. Answers may vary.
2
Set up,but do not evaluate,a double integral for the area of the surface with parametric equations Set up,but do not evaluate,a double integral for the area of the surface with parametric equations
3
Match the equation with one of the graphs below. <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)

A) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)
B) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)
C) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)
D) <strong>Match the equation with one of the graphs below.  </strong> A)   B)   C)   D)
4
Find the area of the surface S where S is the part of the surface Find the area of the surface S where S is the part of the surface   that lies inside the cylinder  that lies inside the cylinder Find the area of the surface S where S is the part of the surface   that lies inside the cylinder
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5
Find the area of the surface S where S is the part of the plane Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and   that lies above the triangular region with vertices Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and   Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and   ,and Find the area of the surface S where S is the part of the plane   that lies above the triangular region with vertices     ,and
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