Question 1

r(t) = 4t3 i + (2t + 3)j is the position vector of a particle moving in a plane. Find the speed at t = 1.

Accepted Answer

A)    
B)  12 
C)  24 
D)  0 
E)    
A)    
B)  12 
C)  24 
D)  0 
E)

Question 2

Describe the graph of

Accepted Answer

The answer of Describe the graph of  ...

Question 3

Describe the graph of   .

Accepted Answer

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

Question 4

Let r(t) = (t2 + 2)i + (10 + 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)  1.732i - 1.732j - 1.732k 
A)  2i + 0.707j + 0.707k 
B)  0.707j - 0.707k 
C)  2i + 0.577j + 0.577k 
D)  0.577j - 0.577k 
E)  1.732i - 1.732j - 1.732k

Question 5

If, for an elliptical orbit, rmin = 1025km and e = 0.86, find a, the semimajor axis.

Accepted Answer

A)  7.14 * 1024km 
B)  7.14 *1025km 
C)  13.29 * 1025km 
D)  13.29 * 1024km 
E)  3.64 *1025km 
A)  7.14 * 1024km 
B)  7.14 *1025km 
C)  13.29 * 1025km 
D)  13.29 * 1024km 
E)  3.64 *1025km

Question 6

At t increases, the graph of   sketches

Accepted Answer

A)  Clockwise and up 
B)  Counter-clockwise and up 
C)  Clockwise and down 
D)  Counter-clockwise and down 
E)  In a circle 
A)  Clockwise and up 
B)  Counter-clockwise and up 
C)  Clockwise and down 
D)  Counter-clockwise and down 
E)  In a circle

Question 7

Let r(t) = (t2 + 2)i + e t j + (12 + e t )k. Find N(t) for t = 0.

Accepted Answer

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

r(t) = 4t³ i + (2t + 3)j is the position vector of a particle moving in a plane. Find the speed at t = 1.

Describe the graph of

Describe the graph of .

Let r(t) = (t² + 2)i + (10 + e ^t )j + e ^t k. Find B(t) for t = 0. Approximate your calculations to three decimal places.

If, for an elliptical orbit, r_min = 10²⁵km and e = 0.86, find a, the semimajor axis.

At t increases, the graph of sketches

Let r(t) = (t² + 2)i + e ^t j + (12 + e ^t )k. Find N(t) for t = 0.

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

r(t) = 4t3 i + (2t + 3)j is the position vector of a particle moving in a plane. Find the speed at t = 1.

Describe the graph of

Describe the graph of .

Let r(t) = (t2 + 2)i + (10 + e t )j + e t k. Find B(t) for t = 0. Approximate your calculations to three decimal places.

If, for an elliptical orbit, rmin = 1025km and e = 0.86, find a, the semimajor axis.

At t increases, the graph of sketches

Let r(t) = (t2 + 2)i + e t j + (12 + e t )k. Find N(t) for t = 0.

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

r(t) = 4t³ i + (2t + 3)j is the position vector of a particle moving in a plane. Find the speed at t = 1.

Let r(t) = (t² + 2)i + (10 + e ^t )j + e ^t k. Find B(t) for t = 0. Approximate your calculations to three decimal places.

If, for an elliptical orbit, r_min = 10²⁵km and e = 0.86, find a, the semimajor axis.

Let r(t) = (t² + 2)i + e ^t j + (12 + e ^t )k. Find N(t) for t = 0.