Deck 13: Extension H: Vector Calculus

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سؤال
Evaluate the surface integral. <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> S is the part of the plane <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> that lies in the first octant.

A) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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سؤال
Evaluate the surface integral Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.    <div style=padding-top: 35px> for the given vector field F and the oriented surface S.In other words,find the flux of F across S. Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.    <div style=padding-top: 35px> Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.    <div style=padding-top: 35px>
سؤال
Evaluate the surface integral.Round your answer to four decimal places. <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> S is surface <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone   if its density function is   <div style=padding-top: 35px> if its density function is Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone   if its density function is   <div style=padding-top: 35px>
سؤال
Use Gauss's Law to find the charge contained in the solid hemisphere Use Gauss's Law to find the charge contained in the solid hemisphere   ,if the electric field is  <div style=padding-top: 35px> ,if the electric field is Use Gauss's Law to find the charge contained in the solid hemisphere   ,if the electric field is  <div style=padding-top: 35px>
سؤال
Evaluate the surface integral Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.   in the first octant,with orientation toward the origin.<div style=padding-top: 35px> for the given vector field F and the oriented surface S.In other words,find the flux of F across S. Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.   in the first octant,with orientation toward the origin.<div style=padding-top: 35px> in the first octant,with orientation toward the origin.
سؤال
Suppose that <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px> where g is a function of one variable such that <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px> Evaluate <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px> where S is the sphere <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>

A) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
B) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
C) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
D) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
E) None of these
سؤال
The temperature at the point <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> in a substance with conductivity <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> Find the rate of heat flow inward across the cylindrical <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A fluid with density A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid   <div style=padding-top: 35px> flows with velocity A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid   <div style=padding-top: 35px> Find the rate of flow upward through the paraboloid A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid   <div style=padding-top: 35px>
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Deck 13: Extension H: Vector Calculus
1
Evaluate the surface integral. <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   S is the part of the plane <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)   that lies in the first octant.

A) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)
B) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)
C) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)
D) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)
E) <strong>Evaluate the surface integral.   S is the part of the plane   that lies in the first octant.</strong> A)   B)   C)   D)   E)
2
Evaluate the surface integral Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.    for the given vector field F and the oriented surface S.In other words,find the flux of F across S. Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.    Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.
144
3
Evaluate the surface integral.Round your answer to four decimal places. <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)   S is surface <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)

A) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)
B) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)
C) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)
D) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)
E) <strong>Evaluate the surface integral.Round your answer to four decimal places.   S is surface  </strong> A)   B)   C)   D)   E)
4
Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone   if its density function is   if its density function is Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone   if its density function is
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5
Use Gauss's Law to find the charge contained in the solid hemisphere Use Gauss's Law to find the charge contained in the solid hemisphere   ,if the electric field is  ,if the electric field is Use Gauss's Law to find the charge contained in the solid hemisphere   ,if the electric field is
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6
Evaluate the surface integral Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.   in the first octant,with orientation toward the origin. for the given vector field F and the oriented surface S.In other words,find the flux of F across S. Evaluate the surface integral   for the given vector field F and the oriented surface S.In other words,find the flux of F across S.   in the first octant,with orientation toward the origin. in the first octant,with orientation toward the origin.
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7
Suppose that <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these where g is a function of one variable such that <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these Evaluate <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these where S is the sphere <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these

A) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these
B) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these
C) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these
D) <strong>Suppose that   where g is a function of one variable such that   Evaluate   where S is the sphere  </strong> A)   B)   C)   D)   E) None of these
E) None of these
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8
The temperature at the point <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   in a substance with conductivity <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   is <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)   Find the rate of heat flow inward across the cylindrical <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)

A) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)
B) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)
C) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)
D) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)
E) <strong>The temperature at the point   in a substance with conductivity   is   Find the rate of heat flow inward across the cylindrical  </strong> A)   B)   C)   D)   E)
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A fluid with density A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid   flows with velocity A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid   Find the rate of flow upward through the paraboloid A fluid with density   flows with velocity   Find the rate of flow upward through the paraboloid
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