Deck 10: Extension G: Vector Functions

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Question
Find the curvature of the curve <strong>Find the curvature of the curve  </strong> A) 11 B)   C) 1 D) 0 <div style=padding-top: 35px>

A) 11
B) <strong>Find the curvature of the curve  </strong> A) 11 B)   C) 1 D) 0 <div style=padding-top: 35px>
C) 1
D) 0
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Question
Find the length of the curve <strong>Find the length of the curve    </strong> A)   B)   C)   D)   <div style=padding-top: 35px> <strong>Find the length of the curve    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the length of the curve    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the length of the curve    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the length of the curve    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the length of the curve    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
Question
Reparametrize the curve with respect to arc length measured from the point where <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> in the direction of increasing <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the curvature of the curve <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
Question
For the curve given by <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px> ,find the unit normal vector. <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>

A) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
B) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
C) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
D) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
E) None of these
Question
The curvature of the curve given by the vector function <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> Use the formula to find the curvature of <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> at the point <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the length of the curve <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px>

A) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
B) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
C) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
D) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
Question
At what point on the curve <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is the normal plane parallel to the plane <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> ?

A) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the curvature of <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 10: Extension G: Vector Functions
1
Find the curvature of the curve <strong>Find the curvature of the curve  </strong> A) 11 B)   C) 1 D) 0

A) 11
B) <strong>Find the curvature of the curve  </strong> A) 11 B)   C) 1 D) 0
C) 1
D) 0
0
2
Find the length of the curve <strong>Find the length of the curve    </strong> A)   B)   C)   D)   <strong>Find the length of the curve    </strong> A)   B)   C)   D)

A) <strong>Find the length of the curve    </strong> A)   B)   C)   D)
B) <strong>Find the length of the curve    </strong> A)   B)   C)   D)
C) <strong>Find the length of the curve    </strong> A)   B)   C)   D)
D) <strong>Find the length of the curve    </strong> A)   B)   C)   D)
3
Reparametrize the curve with respect to arc length measured from the point where <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   in the direction of increasing <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)   <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)

A) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)
B) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)
C) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)
D) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)
E) <strong>Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing    </strong> A)   B)   C)   D)   E)
4
Find the curvature of the curve <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)

A) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)
B) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)
C) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)
D) <strong>Find the curvature of the curve  </strong> A)   B)   C)   D)
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5
For the curve given by <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these ,find the unit normal vector. <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these

A) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these
B) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these
C) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these
D) <strong>For the curve given by   ,find the unit normal vector.  </strong> A)   B)   C)   D)   E) None of these
E) None of these
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6
The curvature of the curve given by the vector function <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   is <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   Use the formula to find the curvature of <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)   at the point <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)

A) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)
B) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)
C) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)
D) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)
E) <strong>The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point  </strong> A)   B)   C)   D)   E)
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7
Find the length of the curve <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <strong>Find the length of the curve    </strong> A)     B)     C)     D)

A) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <strong>Find the length of the curve    </strong> A)     B)     C)     D)
B) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <strong>Find the length of the curve    </strong> A)     B)     C)     D)
C) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <strong>Find the length of the curve    </strong> A)     B)     C)     D)
D) <strong>Find the length of the curve    </strong> A)     B)     C)     D)     <strong>Find the length of the curve    </strong> A)     B)     C)     D)
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8
At what point on the curve <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   is the normal plane parallel to the plane <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)   ?

A) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)
B) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)
C) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)
D) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)
E) <strong>At what point on the curve   is the normal plane parallel to the plane   ?</strong> A)   B)   C)   D)   E)
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9
Find the curvature of <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)

A) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)
B) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)
C) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)
D) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)
E) <strong>Find the curvature of  </strong> A)   B)   C)   D)   E)
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