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A force with magnitude A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E) N acts directly upward from the xy-plane on an object with mass A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E) kg. The object starts at the origin with initial velocity A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E) . Find its position function.


A) A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E)
B) A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E) A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E) A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E)
C) A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E)
D) A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E)
E) A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function. A) B) C) D) E)

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Sketch the curve of the vector function Sketch the curve of the vector function , and indicate the orientation of the curve. , and indicate the orientation of the curve.

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The helix The helix intersects the curve at the point . Find the angle of intersection. A) B) C) D) E) None of these intersects the curve The helix intersects the curve at the point . Find the angle of intersection. A) B) C) D) E) None of these at the point The helix intersects the curve at the point . Find the angle of intersection. A) B) C) D) E) None of these . Find the angle of intersection.


A) The helix intersects the curve at the point . Find the angle of intersection. A) B) C) D) E) None of these
B) The helix intersects the curve at the point . Find the angle of intersection. A) B) C) D) E) None of these
C) The helix intersects the curve at the point . Find the angle of intersection. A) B) C) D) E) None of these
D) The helix intersects the curve at the point . Find the angle of intersection. A) B) C) D) E) None of these
E) None of these

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Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. A) B) C) D) E)


A) Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. A) B) C) D) E)
B) Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. A) B) C) D) E)
C) Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. A) B) C) D) E)
D) Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. A) B) C) D) E)
E) Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. A) B) C) D) E)

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Find the domain of the vector function Find the domain of the vector function . A) B) C) D) .


A) Find the domain of the vector function . A) B) C) D)
B) Find the domain of the vector function . A) B) C) D)
C) Find the domain of the vector function . A) B) C) D)
D) Find the domain of the vector function . A) B) C) D)

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The figure shows a curve The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E) given by a vector function The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E) . Choose the correct expression for The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E) . The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E)


A) The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E)
B) The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E)
C) The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E)
D) The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E)
E) The figure shows a curve given by a vector function . Choose the correct expression for . A) B) C) D) E)

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A particle moves with position function A particle moves with position function . Find the acceleration of the particle. . Find the acceleration of the particle.

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Find Find and for and Find and for for Find and for

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Find the velocity of a particle with the given position function. Find the velocity of a particle with the given position function. A) B) C) D) E)


A) Find the velocity of a particle with the given position function. A) B) C) D) E)
B) Find the velocity of a particle with the given position function. A) B) C) D) E)
C) Find the velocity of a particle with the given position function. A) B) C) D) E)
D) Find the velocity of a particle with the given position function. A) B) C) D) E)
E) Find the velocity of a particle with the given position function. A) B) C) D) E)

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The torsion of a curve defined by The torsion of a curve defined by is given by Find the torsion of the curve defined by . A) B) C) D) is given by The torsion of a curve defined by is given by Find the torsion of the curve defined by . A) B) C) D) Find the torsion of the curve defined by The torsion of a curve defined by is given by Find the torsion of the curve defined by . A) B) C) D) .


A) The torsion of a curve defined by is given by Find the torsion of the curve defined by . A) B) C) D)
B) The torsion of a curve defined by is given by Find the torsion of the curve defined by . A) B) C) D)
C) The torsion of a curve defined by is given by Find the torsion of the curve defined by . A) B) C) D)
D) The torsion of a curve defined by is given by Find the torsion of the curve defined by . A) B) C) D)

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Find the scalar tangential and normal components of acceleration of a particle with position vector Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) ,


A) Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) , , Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) ,
B) Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) , , Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) ,
C) Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) , , Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) ,
D) Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) , , Find the scalar tangential and normal components of acceleration of a particle with position vector A) , B) , C) , D) ,

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Find the length of the curve Find the length of the curve A) B) C) D) Find the length of the curve A) B) C) D)


A) Find the length of the curve A) B) C) D)
B) Find the length of the curve A) B) C) D)
C) Find the length of the curve A) B) C) D)
D) Find the length of the curve A) B) C) D)

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Find the limit Find the limit . A) B) C) D) .


A) Find the limit . A) B) C) D)
B) Find the limit . A) B) C) D)
C) Find the limit . A) B) C) D)
D) Find the limit . A) B) C) D)

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Find the velocity, acceleration, and speed of an object with position function Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors. for Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors. Sketch the path of the object and its velocity and acceleration vectors.

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Find the velocity, acceleration, and speed of an object with position vector Find the velocity, acceleration, and speed of an object with position vector . .

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Find Find if and . if Find if and . and Find if and . .

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Find the limit Find the limit . .

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Find the curvature of the curve Find the curvature of the curve . A) B) C) D) .


A) Find the curvature of the curve . A) B) C) D)
B) Find the curvature of the curve . A) B) C) D)
C) Find the curvature of the curve . A) B) C) D)
D) Find the curvature of the curve . A) B) C) D)

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Find the curvature of Find the curvature of . A) B) C) D) E) .


A) Find the curvature of . A) B) C) D) E)
B) Find the curvature of . A) B) C) D) E)
C) Find the curvature of . A) B) C) D) E)
D) Find the curvature of . A) B) C) D) E)
E) Find the curvature of . A) B) C) D) E)

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Find Find if and . A) B) C) D) E) if Find if and . A) B) C) D) E) and Find if and . A) B) C) D) E) .


A) Find if and . A) B) C) D) E)
B) Find if and . A) B) C) D) E)
C) Find if and . A) B) C) D) E)
D) Find if and . A) B) C) D) E)
E) Find if and . A) B) C) D) E)

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