Deck 15: Section 1: Vector Analysis

ملء الشاشة (f)
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سؤال
Find the divergence of the vector field at the given point. <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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سؤال
Find the divergence of the vector field F given by <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Sketch several representative vectors in the vector field given by <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine whether the vector field is conservative. If it is, find a potential function for the vector field. <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>

A) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
B) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
C) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
D) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
E) not conservative
سؤال
Determine whether the vector field is conservative. If it is, find a potential function for the vector field. <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>

A) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
B) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
C) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
D) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
E) not conservative
سؤال
Sketch the vector field <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Match the vector field with its graph. <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine whether the vector field is conservative. <strong>Determine whether the vector field is conservative.  </strong> A) conservative B) not conservative <div style=padding-top: 35px>

A) conservative
B) not conservative
سؤال
Find the conservative vector field for the potential function <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> by finding its gradient.

A) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the divergence of the vector field. <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   .  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine whether the vector field is conservative. If it is, find a potential function for the vector field. <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>

A) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
B) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
C) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
D) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative <div style=padding-top: 35px>
E) not conservative
سؤال
Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the divergence at <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for the vector field <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Match the vector field with its graph <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Compute <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for the vector field given by <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the curl for the vector field at the given point. <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for the vector field given by <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 15: Section 1: Vector Analysis
1
Find the divergence of the vector field at the given point. <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the divergence of the vector field at the given point.  </strong> A)   B)   C)   D)   E)
2
Find the divergence of the vector field F given by <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the divergence of the vector field F given by   .</strong> A)   B)   C)   D)   E)
3
Sketch several representative vectors in the vector field given by <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)
B) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)
C) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)
D) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)
E) <strong>Sketch several representative vectors in the vector field given by   .</strong> A)   B)   C)   D)   E)
4
Find <strong>Find   .  </strong> A)   B)   C)   D)   E)   . <strong>Find   .  </strong> A)   B)   C)   D)   E)

A) <strong>Find   .  </strong> A)   B)   C)   D)   E)
B) <strong>Find   .  </strong> A)   B)   C)   D)   E)
C) <strong>Find   .  </strong> A)   B)   C)   D)   E)
D) <strong>Find   .  </strong> A)   B)   C)   D)   E)
E) <strong>Find   .  </strong> A)   B)   C)   D)   E)
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5
Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)

A) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
B) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
C) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
D) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
E) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
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6
Determine whether the vector field is conservative. If it is, find a potential function for the vector field. <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative

A) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
B) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
C) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
D) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
E) not conservative
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7
Determine whether the vector field is conservative. If it is, find a potential function for the vector field. <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative

A) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
B) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
C) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
D) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
E) not conservative
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8
Sketch the vector field <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)
B) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)
C) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)
D) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)
E) <strong>Sketch the vector field   .</strong> A)   B)   C)   D)   E)
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9
Find <strong>Find   .  </strong> A)   B)   C)   D)   E)   . <strong>Find   .  </strong> A)   B)   C)   D)   E)

A) <strong>Find   .  </strong> A)   B)   C)   D)   E)
B) <strong>Find   .  </strong> A)   B)   C)   D)   E)
C) <strong>Find   .  </strong> A)   B)   C)   D)   E)
D) <strong>Find   .  </strong> A)   B)   C)   D)   E)
E) <strong>Find   .  </strong> A)   B)   C)   D)   E)
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10
Match the vector field with its graph. <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the vector field with its graph.  </strong> A)   B)   C)   D)   E)
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11
Determine whether the vector field is conservative. <strong>Determine whether the vector field is conservative.  </strong> A) conservative B) not conservative

A) conservative
B) not conservative
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12
Find the conservative vector field for the potential function <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)   by finding its gradient.

A) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)
B) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)
C) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)
D) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)
E) <strong>Find the conservative vector field for the potential function   by finding its gradient.</strong> A)   B)   C)   D)   E)
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13
Find the divergence of the vector field. <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the divergence of the vector field.  </strong> A)   B)   C)   D)   E)
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14
Find <strong>Find   .  </strong> A)   B)   C)   D)   E)   . <strong>Find   .  </strong> A)   B)   C)   D)   E)

A) <strong>Find   .  </strong> A)   B)   C)   D)   E)
B) <strong>Find   .  </strong> A)   B)   C)   D)   E)
C) <strong>Find   .  </strong> A)   B)   C)   D)   E)
D) <strong>Find   .  </strong> A)   B)   C)   D)   E)
E) <strong>Find   .  </strong> A)   B)   C)   D)   E)
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15
Determine whether the vector field is conservative. If it is, find a potential function for the vector field. <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative

A) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
B) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
C) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
D) conservative with potential function <strong>Determine whether the vector field is conservative. If it is, find a potential function for the vector field.  </strong> A) conservative with potential function   B) conservative with potential function   C) conservative with potential function   D) conservative with potential function   E) not conservative
E) not conservative
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16
Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)

A) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
B) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
C) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
D) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
E) <strong>Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)  </strong> A)   B)   C)   D)   E)
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17
Find the divergence at <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)   for the vector field <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)

A) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)
B) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)
C) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)
D) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)
E) <strong>Find the divergence at   for the vector field  </strong> A)   B)   C)   D)   E)
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18
Match the vector field with its graph <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)

A) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)
B) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)
C) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)
D) <strong>Match the vector field with its graph  </strong> A)   B)   C)   D)
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19
Compute <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   for the vector field given by <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)
B) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)
C) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)
D) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)
E) <strong>Compute   for the vector field given by   .</strong> A)   B)   C)   D)   E)
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20
Find the curl for the vector field at the given point. <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the curl for the vector field at the given point.  </strong> A)   B)   C)   D)   E)
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21
Find <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   for the vector field given by <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)
B) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)
C) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)
D) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)
E) <strong>Find   for the vector field given by   .</strong> A)   B)   C)   D)   E)
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