Deck 12: Section 2: Vector-Valued Functions

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Question
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Question
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Evaluate the definite integral below. <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the indefinite integral below. <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> Do not include an arbitrary constant vector.

A) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the vectors <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> and <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for the following vector function. <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the indefinite integral below. <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> Do not include an arbitrary constant vector.

A) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the indefinite integral below. <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> Do not include an arbitrary constant vector.

A) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Evaluate the definite integral below. <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the vector-valued function below. <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the open interval on which the curve given by the vector-valued function <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is smooth.

A) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)   <div style=padding-top: 35px> given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)   <div style=padding-top: 35px>

A) 2
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)   <div style=padding-top: 35px>
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)   <div style=padding-top: 35px>
D) 5
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)   <div style=padding-top: 35px>
Question
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3   <div style=padding-top: 35px> given the following vector function. <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3   <div style=padding-top: 35px>

A) cost sint
B) -34 <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3   <div style=padding-top: 35px>
C) 34 <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3   <div style=padding-top: 35px>
D) -16 sin t cos t
E) 3 <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3   <div style=padding-top: 35px>
Question
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following vector function: <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
A particle moves in the yz-plane along the curve represented by the vector-valued function <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the minimum value of   .</strong> A) 6 B) 4 C) 7 D) 9 E) 8 <div style=padding-top: 35px> . Find the minimum value of <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the minimum value of   .</strong> A) 6 B) 4 C) 7 D) 9 E) 8 <div style=padding-top: 35px> .

A) 6
B) 4
C) 7
D) 9
E) 8
Question
Find <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following. <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
A particle moves in the yz-plane along the curve represented by the vector-valued function <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the maximum value of   .</strong> A) 4 B) 3 C) 7 D) 8 E) 5 <div style=padding-top: 35px> . Find the maximum value of <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the maximum value of   .</strong> A) 4 B) 3 C) 7 D) 8 E) 5 <div style=padding-top: 35px> .

A) 4
B) 3
C) 7
D) 8
E) 5
Question
Find <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> given the following. <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 12: Section 2: Vector-Valued Functions
1
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
2
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
3
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
4
Evaluate the definite integral below. <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)

A) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
B) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
C) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
D) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
E) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
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5
Find the indefinite integral below. <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   Do not include an arbitrary constant vector.

A) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
B) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
C) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
D) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
E) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
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6
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
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7
Find the vectors <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   and <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)   for the following vector function. <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the vectors   and   for the following vector function.  </strong> A)   B)   C)   D)   E)
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8
Find the indefinite integral below. <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   Do not include an arbitrary constant vector.

A) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
B) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
C) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
D) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
E) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
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9
Find the indefinite integral below. <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)   Do not include an arbitrary constant vector.

A) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
B) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
C) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
D) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
E) <strong>Find the indefinite integral below.   Do not include an arbitrary constant vector.</strong> A)   B)   C)   D)   E)
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10
Evaluate the definite integral below. <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)

A) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
B) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
C) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
D) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
E) <strong>Evaluate the definite integral below.  </strong> A)   B)   C)   D)   E)
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11
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)   given the vector-valued function below. <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)

A) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)
B) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)
C) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)
D) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)
E) <strong>Use the properties of the derivative to find   given the vector-valued function below.  </strong> A)   B)   C)   D)   E)
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12
Find the open interval on which the curve given by the vector-valued function <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)   is smooth.

A) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)
B) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)
C) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)
D) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)
E) <strong>Find the open interval on which the curve given by the vector-valued function   is smooth.</strong> A)   B)   C)   D)   E)
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13
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)   given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)

A) 2
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)
D) 5
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A) 2 B)   C)   D) 5 E)
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14
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
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15
Find <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3   given the following vector function. <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3

A) cost sint
B) -34 <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3
C) 34 <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3
D) -16 sin t cos t
E) 3 <strong>Find   given the following vector function.  </strong> A) cost sint B) -34   C) 34   D) -16 sin t cos t E) 3
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16
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
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17
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
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18
Find <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)   given the following vector function. <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following vector function.  </strong> A)   B)   C)   D)   E)
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19
Use the properties of the derivative to find <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)   given the following vector-valued functions. <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)

A) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
B) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
C) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
D) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
E) <strong>Use the properties of the derivative to find   given the following vector-valued functions.  </strong> A)   B)   C)   D)   E)
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20
Find <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)   given the following vector function: <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following vector function:  </strong> A)   B)   C)   D)   E)
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21
A particle moves in the yz-plane along the curve represented by the vector-valued function <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the minimum value of   .</strong> A) 6 B) 4 C) 7 D) 9 E) 8 . Find the minimum value of <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the minimum value of   .</strong> A) 6 B) 4 C) 7 D) 9 E) 8 .

A) 6
B) 4
C) 7
D) 9
E) 8
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22
Find <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   given the following. <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
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23
A particle moves in the yz-plane along the curve represented by the vector-valued function <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the maximum value of   .</strong> A) 4 B) 3 C) 7 D) 8 E) 5 . Find the maximum value of <strong>A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the maximum value of   .</strong> A) 4 B) 3 C) 7 D) 8 E) 5 .

A) 4
B) 3
C) 7
D) 8
E) 5
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24
Find <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)   given the following. <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)

A) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
B) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
C) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
D) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
E) <strong>Find   given the following.  </strong> A)   B)   C)   D)   E)
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