Question 1

Describe the graph of   .

Accepted Answer

A)  Twisted cubic 
B)  Single point 
C)  Spiral 
D)  Parabola 
E)  Circle 
A)  Twisted cubic 
B)  Single point 
C)  Spiral 
D)  Parabola 
E)  Circle

Question 2

Let r(t) = (t3 + 2)i + te t j + (7 + e t )k. Find N(t) for t = 0.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Let r(t) = (t3 + 2)i + te t j + (9 + e t )k. Find T(t) for t = 0.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Find the curvature for   at t = 0.

Accepted Answer

The answer of Find the curvature for   at...

Question 5

If v = 2i and a = 5i - 7j, find aT .

Accepted Answer

A)  5 
B)  6 
C)    
D)  8 
E)  9 
A)  5 
B)  6 
C)    
D)  8 
E)  9

Question 6

Let r(t) = 3t2 i + (4 + 4t2)j + 6t k. Find B(t).

Accepted Answer

A)    
B)  0 
C)    
D)    
E)  i + j + k 
A)    
B)  0 
C)    
D)    
E)  i + j + k

Question 7

Find the arc length of the graph of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the curvature   for

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

A shell is fired from a mortar at ground level with a velocity of 200 meters per second at an elevation of 60°. How far does the shell travel horizontally?

Accepted Answer

The answer of A shell is fired from a mortar...

Question 10

Describe the graph of   .

Accepted Answer

A)  Twisted cubic 
B)  Straight line 
C)  Spiral 
D)  Parabola 
E)  Circle 
A)  Twisted cubic 
B)  Straight line 
C)  Spiral 
D)  Parabola 
E)  Circle

Question 11

Find the arc length of the graph of

Accepted Answer

A)  3 
B)    
C)  8.307 
D)    
E)    
A)  3 
B)    
C)  8.307 
D)    
E)

Question 12

The position vector of a particle moving in a plane is given by   . Find the velocity.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Let   . Find the equation of the line tangent to the graph of   at the point when   . Write your answer using parametric equations.

Accepted Answer

The answer of Let   . Find the equation...

Question 14

If   and   , then k(t) at t = 0 is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find the arc length of the graph of

Accepted Answer

The answer of Find the arc length of the graph...

Question 16

If   find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Let r(t) = (t2 + 2)i + e t j + (   + e t )k. Find B(t) for t = 0. Approximate your calculations to three decimal places.

Accepted Answer

A)  2i + 0.707j + 0.707k 
B)  0.707j - 0.707k 
C)  2i + 0.577j + 0.577k 
D)  0.577j - 0.577k 
E)  1.334i - 1.334j - 1.334k 
A)  2i + 0.707j + 0.707k 
B)  0.707j - 0.707k 
C)  2i + 0.577j + 0.577k 
D)  0.577j - 0.577k 
E)  1.334i - 1.334j - 1.334k

Question 18

Find the curvature for x2 + y2 = 10x + 10 at (2, -4).

Accepted Answer

Question 19

If y = cos x, find the curvature at   .

Accepted Answer

A)  0 
B)  1 
C)  -1 
D)    
E)    
A)  0 
B)  1 
C)  -1 
D)    
E)

Question 20

r(t) = t3 i - 2t j; 1 $\le$  t $\le$ 5. Find the displacement.

Accepted Answer

A)  124i - 8j 
B)  125i - 8j 
C)  124i + 10j 
D)  124i + 8j 
E)  -124i - 8j 
A)  124i - 8j 
B)  125i - 8j 
C)  124i + 10j 
D)  124i + 8j 
E)  -124i - 8j

Describe the graph of .

Let r(t) = (t³ + 2)i + te ^t j + (7 + e ^t )k. Find N(t) for t = 0.

Let r(t) = (t³ + 2)i + te ^t j + (9 + e ^t )k. Find T(t) for t = 0.

Find the curvature for at t = 0.

If v = 2i and a = 5i - 7j, find a_T .

Let r(t) = 3t² i + (4 + 4t²)j + 6t k. Find B(t).

Find the arc length of the graph of

Find the curvature for

A shell is fired from a mortar at ground level with a velocity of 200 meters per second at an elevation of 60°. How far does the shell travel horizontally?

Describe the graph of .

Find the arc length of the graph of

The position vector of a particle moving in a plane is given by . Find the velocity.

Let . Find the equation of the line tangent to the graph of at the point when . Write your answer using parametric equations.

If and , then k(t) at t = 0 is

Find the arc length of the graph of

If find

Let r(t) = (t² + 2)i + e ^t j + ( + e ^t )k. Find B(t) for t = 0. Approximate your calculations to three decimal places.

Find the curvature for x² + y² = 10x + 10 at (2, -4).

If y = cos x, find the curvature at .

r(t) = t³ i - 2t j; 1 $\le$ t $\le$ 5. Find the displacement.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 12: Vector-Valued Functions

Describe the graph of .

Let r(t) = (t3 + 2)i + te t j + (7 + e t )k. Find N(t) for t = 0.

Let r(t) = (t3 + 2)i + te t j + (9 + e t )k. Find T(t) for t = 0.

Find the curvature for at t = 0.

If v = 2i and a = 5i - 7j, find aT .

Let r(t) = 3t2 i + (4 + 4t2)j + 6t k. Find B(t).

Find the arc length of the graph of

Find the curvature for

A shell is fired from a mortar at ground level with a velocity of 200 meters per second at an elevation of 60°. How far does the shell travel horizontally?

Describe the graph of .

Find the arc length of the graph of

The position vector of a particle moving in a plane is given by . Find the velocity.

Let . Find the equation of the line tangent to the graph of at the point when . Write your answer using parametric equations.

If and , then k(t) at t = 0 is

Find the arc length of the graph of

If find

Let r(t) = (t2 + 2)i + e t j + ( + e t )k. Find B(t) for t = 0. Approximate your calculations to three decimal places.

Find the curvature for x2 + y2 = 10x + 10 at (2, -4).

If y = cos x, find the curvature at .

r(t) = t3 i - 2t j; 1 ≤\le≤ t ≤\le≤ 5. Find the displacement.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Let r(t) = (t³ + 2)i + te ^t j + (7 + e ^t )k. Find N(t) for t = 0.

Let r(t) = (t³ + 2)i + te ^t j + (9 + e ^t )k. Find T(t) for t = 0.

If v = 2i and a = 5i - 7j, find a_T .

Let r(t) = 3t² i + (4 + 4t²)j + 6t k. Find B(t).

Let r(t) = (t² + 2)i + e ^t j + ( + e ^t )k. Find B(t) for t = 0. Approximate your calculations to three decimal places.

Find the curvature for x² + y² = 10x + 10 at (2, -4).

r(t) = t³ i - 2t j; 1 $\le$ t $\le$ 5. Find the displacement.