Question 1

Where is   continuous?

Accepted Answer

A)    
B)    
C)    
D)  4 
E)  0 
A)    
B)    
C)    
D)  4 
E)  0

Question 2

Find the speed of a particle moving along the curve r(t) = (13 + t3)i + 4t j - t2 k at t = 1.

Accepted Answer

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

Question 3

If   , find k(s).

Accepted Answer

A)    
B)    
C)  2 
D)  4 
E)  0 
A)    
B)    
C)  2 
D)  4 
E)  0

Question 4

Sketch x = 2 cos t, y = 3 sin t for 0$\le$t $\le$ 2 $\pi$. Calculate the radius of curvature at   and sketch the oscillating circle.

Accepted Answer

The answer of Sketch x = 2 cos t, y...

Question 5

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

Accepted Answer

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

Question 6

Find the parametric equations that correspond to the given vector equation:   .

Accepted Answer

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

Question 7

Find the acceleration of a particle moving along the curve r(t) = t3 i + (8 + 4t)j - t2 k at t = 1.

Accepted Answer

A)  3i + 4j - 2k 
B)  6i - 2k 
C)  3i + 4j + 2k 
D)  0 
E)  3i - 4j - 2k 
A)  3i + 4j - 2k 
B)  6i - 2k 
C)  3i + 4j + 2k 
D)  0 
E)  3i - 4j - 2k

Question 8

Find the curvature   for r(t) = 17i + 2t j + 3t2 k at t = 0.

Accepted Answer

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

Question 9

Describe the graph of

Accepted Answer

The answer of Describe the graph of  ...

Question 10

Find the arc length parameterization of the line   that has the same orientation as the given curve and uses   as a reference point.

Accepted Answer

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

Question 11

Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0.

Accepted Answer

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

Question 12

Let r(t) = (-9 + t) i + t2 j + t3 k. Find T(t) when t = 0.

Accepted Answer

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

Question 13

Find the unit tangent and unit normal vectors to r(t) = t i + ln(cos t) j at   .

Accepted Answer

The answer of Find the unit tangent and unit normal...

Question 14

Find the unit tangent and unit normal vectors to the curve r(t) = 2 sin t i + 3 cos t j at   . Sketch a portion of the curve showing the point of tangency.

Accepted Answer

The answer of Find the unit tangent and unit normal...

Question 15

Describe the graph of

Accepted Answer

The answer of Describe the graph of  ...

Question 16

Let r(t) = (t2 + 2)i + e 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 17

Find the arc length of the graph of

Accepted Answer

A)    
B)    
C)  0 
D)  1 
E)  4 
A)    
B)    
C)  0 
D)  1 
E)  4

Question 18

If   find

Accepted Answer

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

Question 19

Find the speed of a particle in a circular orbit with radius 1022m around an object of mass 1023kg. (G = 6.67 *10-11m/kg·s2)

Accepted Answer

A)  1.50 *109 m/s 
B)  6.67 * 10-10 m/s 
C)  3.87 * 104 m/s 
D)  2.58 *10-5 m/s 
E)  4.91*10-5m/s 
A)  1.50 *109 m/s 
B)  6.67 * 10-10 m/s 
C)  3.87 * 104 m/s 
D)  2.58 *10-5 m/s 
E)  4.91*10-5m/s

Question 20

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

Where is continuous?

Find the speed of a particle moving along the curve r(t) = (13 + t³)i + 4t j - t² k at t = 1.

If , find k(s).

Sketch x = 2 cos t, y = 3 sin t for 0 $\le$ t $\le$ 2 $\pi$ . Calculate the radius of curvature at $Sketch x = 2 cos t, y = 3 sin t for 0 \le t \le 2 \pi . Calculate the radius of curvature at and sketch the oscillating circle.$ and sketch the oscillating circle.

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

Find the parametric equations that correspond to the given vector equation: .

Find the acceleration of a particle moving along the curve r(t) = t³ i + (8 + 4t)j - t² k at t = 1.

Find the curvature for r(t) = 17i + 2t j + 3t² k at t = 0.

Describe the graph of

Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point.

Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0.

Let r(t) = (-9 + t) i + t² j + t³ k. Find T(t) when t = 0.

Find the unit tangent and unit normal vectors to r(t) = t i + ln(cos t) j at .

Find the unit tangent and unit normal vectors to the curve r(t) = 2 sin t i + 3 cos t j at . Sketch a portion of the curve showing the point of tangency.

Describe the graph of

Let r(t) = (t² + 2)i + e ^t j + (9 + e ^t )k. Find T(t) for t = 0.

Find the arc length of the graph of

If find

Find the speed of a particle in a circular orbit with radius 10²²m around an object of mass 10²³kg. (G = 6.67 *10^-11m/kg·s²)

At t increases, the graph of sketches

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

Where is continuous?

Find the speed of a particle moving along the curve r(t) = (13 + t3)i + 4t j - t2 k at t = 1.

If , find k(s).

Sketch x = 2 cos t, y = 3 sin t for 0 ≤\le≤ t ≤\le≤ 2 π\piπ . Calculate the radius of curvature at and sketch the oscillating circle.

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

Find the parametric equations that correspond to the given vector equation: .

Find the acceleration of a particle moving along the curve r(t) = t3 i + (8 + 4t)j - t2 k at t = 1.

Find the curvature for r(t) = 17i + 2t j + 3t2 k at t = 0.

Describe the graph of

Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point.

Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0.

Let r(t) = (-9 + t) i + t2 j + t3 k. Find T(t) when t = 0.

Find the unit tangent and unit normal vectors to r(t) = t i + ln(cos t) j at .

Find the unit tangent and unit normal vectors to the curve r(t) = 2 sin t i + 3 cos t j at . Sketch a portion of the curve showing the point of tangency.

Describe the graph of

Let r(t) = (t2 + 2)i + e t j + (9 + e t )k. Find T(t) for t = 0.

Find the arc length of the graph of

If find

Find the speed of a particle in a circular orbit with radius 1022m around an object of mass 1023kg. (G = 6.67 *10-11m/kg·s2)

At t increases, the graph of sketches

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

Find the speed of a particle moving along the curve r(t) = (13 + t³)i + 4t j - t² k at t = 1.

Sketch x = 2 cos t, y = 3 sin t for 0 $\le$ t $\le$ 2 $\pi$ . Calculate the radius of curvature at $Sketch x = 2 cos t, y = 3 sin t for 0 \le t \le 2 \pi . Calculate the radius of curvature at and sketch the oscillating circle.$ and sketch the oscillating circle.

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

Find the acceleration of a particle moving along the curve r(t) = t³ i + (8 + 4t)j - t² k at t = 1.

Find the curvature for r(t) = 17i + 2t j + 3t² k at t = 0.

Let r(t) = (-9 + t) i + t² j + t³ k. Find T(t) when t = 0.

Let r(t) = (t² + 2)i + e ^t j + (9 + e ^t )k. Find T(t) for t = 0.

Find the speed of a particle in a circular orbit with radius 10²²m around an object of mass 10²³kg. (G = 6.67 *10^-11m/kg·s²)