Deck 13: Extension B: Vector Calculus

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سؤال
Find the exact mass of a thin wire in the shape of the helix <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> if the density is 5.

A) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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سؤال
Evaluate the line integral over the given curve C. Evaluate the line integral over the given curve C.   ,where C is the line segment joining (-2,-1)to (4,5)<div style=padding-top: 35px> ,where C is the line segment joining (-2,-1)to (4,5)
سؤال
Evaluate the line integral over the given curve C.
<strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px> ; <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px> , <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px>

A) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px>
B) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px> <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px>
C) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px>
D) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px> <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <div style=padding-top: 35px>
سؤال
Find the work done by the force field <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> on a particle that moves along the parabola <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the work done by the force field Find the work done by the force field   in moving an object along an arch of the cycloid  <div style=padding-top: 35px> in moving an object along an arch of the cycloid Find the work done by the force field   in moving an object along an arch of the cycloid  <div style=padding-top: 35px>
سؤال
A thin wire is bent into the shape of a semicircle <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> If the linear density is <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> ,find the exact mass of the wire.

A) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> where C is the right half of the circle <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 13: Extension B: Vector Calculus
1
Find the exact mass of a thin wire in the shape of the helix <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)   if the density is 5.

A) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)
B) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)
C) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)
D) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)
E) <strong>Find the exact mass of a thin wire in the shape of the helix   if the density is 5.</strong> A)   B)   C)   D)   E)
2
Evaluate the line integral over the given curve C. Evaluate the line integral over the given curve C.   ,where C is the line segment joining (-2,-1)to (4,5) ,where C is the line segment joining (-2,-1)to (4,5)
3
Evaluate the line integral over the given curve C.
<strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     ; <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     , <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)

A) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)
B) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)
C) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)
D) <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)     <strong>Evaluate the line integral over the given curve C.   ;   ,  </strong> A)   B)     C)   D)
4
Find the work done by the force field <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)   on a particle that moves along the parabola <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)

A) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)
B) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)
C) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)
D) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)
E) <strong>Find the work done by the force field   on a particle that moves along the parabola  </strong> A)   B)   C)   D)   E)
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5
Find the work done by the force field Find the work done by the force field   in moving an object along an arch of the cycloid  in moving an object along an arch of the cycloid Find the work done by the force field   in moving an object along an arch of the cycloid
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6
A thin wire is bent into the shape of a semicircle <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   If the linear density is <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)   ,find the exact mass of the wire.

A) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)
B) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)
C) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)
D) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)
E) <strong>A thin wire is bent into the shape of a semicircle   If the linear density is   ,find the exact mass of the wire.</strong> A)   B)   C)   D)   E)
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Evaluate <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)   where C is the right half of the circle <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)

A) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)
B) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)
C) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)
D) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)
E) <strong>Evaluate   where C is the right half of the circle  </strong> A)   B)   C)   D)   E)
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