Deck 13: Vector Functions

Question 1

Find

Answer 1

Question 2

Find the limit

Answer 2

Question 3

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

Answer 3

Question 4

Find the velocity and position vectors of an object with acceleration initial velocity

Question 5

Find the scalar tangential and normal components of acceleration of a particle with position vector

Question 6

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

Question 7

Find the derivative of the vector function.

Question 8

Find the position vector of a particle that has the given acceleration and the given initial velocity and position.

Question 9

Find equations of the normal plane to

Question 10

A particle moves with position function Find the normal component of the acceleration vector.

Question 11

Find the following limit.

Question 12

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

Question 13

The curves intersects at the origin.Find their angle of intersection correct to the nearest degree.

Question 14

Find the point of intersection of the tangent lines to the curve at the points where

Question 15

Find an expression for

Question 16

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

Question 17

Find the integral

Question 18

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.

Question 19

Find the unit tangent and unit normal vectors for the curve C defined by Sketch the graph of C

Question 20

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

Question 21

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

Question 22

Find the velocity and position vectors of an object with acceleration initial velocity and initial position

Question 23

Sketch the curve of the vector function nd indicate the orientation of the curve.

Question 24

Find an expression for

Question 25

Find the integral

Question 26

for the function given.

Question 27

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

Question 28

Find the derivative

Question 29

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.

Question 30

Find equations of the normal plane to at the point (2, 4, 8).

Question 31

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

Question 32

Given a.Find b.Sketch the curve defined by r and the vectors and on the same set of axes.

Question 33

Find

Question 34

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

Question 35

Find a vector function describing the curve of intersection of the cylinder and the plane

Question 36

Find

Question 37

Find the arc length function for the curve defined by Then use this result to find a parametrization of C in terms of s.

Question 38

Find the limit

Question 39

A projectile is fired from a height of 350 ft with an initial speed of 200 ft/sec and an angle of elevation of a.What are the scalar tangential and normal components of acceleration of the projectile?
b.What are the scalar tangential and normal components of acceleration of the projectile when the projectile is at its maximum height?

Question 40

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

Question 41

Select the correct Answer: for each question.
Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing .

A)
B)
C)
D)
E)

Question 42

Select the correct Answer: for each question.
Let Find the domain of

A)
B)
C)
D)
E)

Question 43

Select the correct Answer: for each question.
A mortar shell is fired with a muzzle speed of 250 ft/sec.Find the angle of elevation of the mortar if the shell strikes a target located 1100 ft away.Round yourAnswer to 2 decimal places.

A)
B)
C)
D)

Question 44

Select the correct Answer: for each question.
Find the unit tangent vector for the curve given by

A)
B)
C)
D)
E)None of these

Question 45

Select the correct Answer: for each question.
The following table gives coordinates of a particle moving through space along a smooth curve. Find the average velocity over the time interval

A)
B)
C)
D)
E)

Question 46

Select the correct Answer: for each question.
Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations from Round yourAnswer to four decimal places.

A)
B)
C)
D)
E)None of these

Question 47

Select the correct Answer: for each question.
Find the speed of a particle with the given position function.

A)
B)
C)
D)
E)

Question 48

Select the correct Answer: for each question.
Find the velocity of a particle with the given position function.

A)
B)
C)
D)
E)

Question 49

Select the correct Answer: for each question.
Find the length of the curve

A)
B)
C)
D)

Question 50

Select the correct Answer: for each question.
Find the limit.

A)
B)
C)
D)
E)

Question 51

Select the correct Answer: for each question.
Find a vector function that represents the curve of intersection of the two surfaces: the top half of the ellipsoid and the parabolic cylinder

A)
B)
C)
D)
E)

Question 52

Select the correct Answer: for each question.
Find parametric equations for the tangent line to the curve with parametric equations at the point with

A)
B)
C)
D)

Question 53

Select the correct Answer: for each question.
The torsion of a curve defined by is given by Find the torsion of the curve defined by

A)
B)
C)
D)

Question 54

Select the correct Answer: for each question.
The helix intersects the curve at the point Find the angle of intersection.

A)
B)
C)
D)
E)None of these

Question 55

Select the correct Answer: for each question.
Find a vector function that represents the curve of intersection of the two surfaces: The circular cylinder and the parabolic cylinder

A)
B)
C)
D)
E)

Question 56

Select the correct Answer: for each question.
Find the domain of the vector function

A)
B)
C)
D)

Question 57

Select the correct Answer: for each question.
A projectile is fired with an initial speed of and angle of elevation Find the range of the projectile.

A)
B)
C)
D)
E)

Question 58

Select the correct Answer: for each question.
The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point

A)
B)
C)
D)
E)

Question 59

Select the correct Answer: for each question.
If

A)
B)
C)
D)
E)

Question 60

Select the correct Answer: for each question.
Find the scalar tangential and normal components of acceleration of a particle with position vector

A)
B)
C)
D)

Question 61

Select the correct Answer for each question.
Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing

A)
B)
C)
D)
E)

Question 62

Select the correct Answer for each question.
Find the curvature of the curve

A)
B)
C)
D)

Question 63

Select the correct Answer for each question.
Find the length of the curve

A)
B)
C)
D)

Question 64

Select the correct Answer for each question.
Find for the function given.

A)
B)
C)
D)
E)

Question 65

Select the correct Answer for each question.
Find the limit

A)
B)
C)
D)

Question 66

Select the correct Answer for each question.
A ball is thrown at an angle of to the ground.If the ball lands m away, what was the initial speed of the ball? Let

A)
B)
C)
D)
E)

Question 67

Select the correct Answer for each question.
Find the speed of a particle with the given position function.

A)
B)
C)
D)
E)

Question 68

Select the correct Answer for each question.
Find the scalar tangential and normal components of acceleration of a particle with position vector

A)
B)
C)
D)

Question 69

Select the correct Answer for each question.
Find satisfying the conditions for

A)
B)
C)
D)

Question 70

Select the correct Answer for each question.
At what point on the curve is the normal plane parallel to the plane

A)
B)
C)
D)
E)

Question 71

Select the correct Answer for each question.
If

A)
B)
C)
D)
E)

Question 72

Select the correct Answer for each question.
Find a vector function that represents the curve of intersection of the two surfaces: the top half of the ellipsoid and the parabolic cylinder

A)
B)
C)
D)
E)

Question 73

Select the correct Answer for each question.
What force is required so that a particle of mass has the following position function?.

A)
B)
C)
D)
E)

Question 74

Select the correct Answer for each question.
If

A)
B)
C)
D)
E)

Question 75

Select the correct Answer for each question.
The torsion of a curve defined by is given by Find the torsion of the curve defined by

A)
B)
C)
D)

Question 76

Select the correct Answer for each question.
A particle moves with position function Find the tangential component of the acceleration vector.

A)
B)
C)
D)
E)

Question 77

Select the correct Answer for each question.
Find the scalar tangential and normal components of acceleration of a particle with position vector

A)
B)
C)
D)

Question 78

Select the correct Answer for each question.
Find the integral

A)
B)
C)
D)

Question 79

Select the correct Answer for each question.
Let C be a smooth curve defined by and let and be the unit tangent vector and unit normal vector to C corresponding to t.The plane determined by T and N is called the osculating plane.Find an equation of the osculating plane of the curve described by at

A)
B)
C)
D)

Question 80

Select the correct Answer for each question.
Find the length of the curve

A)
B)
C)
D)