Question 1

Find the arc length of the graph of

Accepted Answer

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

Question 2

If   , find   when t = 1.

Accepted Answer

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

Question 3

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 E

Question 4

Where is   continuous?

Accepted Answer

A)    
B)    
C)    
D)  11 
E)  0 
A)    
B)    
C)    
D)  11 
E)  0

Question 5

A particle travels along a curve given by r(t) = 7 cos 3t i - 7 sin 3t j + 2k. Find the distance traveled by the particle during the time interval   seconds.

Accepted Answer

The answer of A particle travels along a curve given...

Question 6

Find the domain of

Accepted Answer

The answer of Find the domain of  ...

Question 7

An object in an elliptical orbit has   and   Find rmax.

Accepted Answer

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

Question 8

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 9

Find the arc length of the graph of

Accepted Answer

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

Question 10

Find the domain of   and calculate   .

Accepted Answer

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

Question 11

At what point does   have maximum curvature?

Accepted Answer

A)  (0, -4) 
B)  (-1, 0) 
C)  (-5, 0) 
D)  (0, 0) 
E)  (0, 1) 
A)  (0, -4) 
B)  (-1, 0) 
C)  (-5, 0) 
D)  (0, 0) 
E)  (0, 1)

Question 12

Given G = 6.67 * 10-11 m3/kg·s2, find the radius of a circular orbit above a 1050-kg mass, if the orbiting object has a speed of 51 m/s.

Accepted Answer

The answer of Given G = 6.67 * 10-11 m3/kg·s2,...

Question 13

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

Accepted Answer

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

Question 14

Find the arc length of the parametric curve

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

r(t) = 3t i + 6t j + 7t k is the position vector of a particle moving in a plane. Find the acceleration of the particle.

Accepted Answer

A)  3i + 6j + 9k 
B)  18 
C)  0 
D)  i + j + k 
E)  3i - 6j - 9k 
A)  3i + 6j + 9k 
B)  18 
C)  0 
D)  i + j + k 
E)  3i - 6j - 9k

Question 17

If   find

Accepted Answer

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

Question 18

Find the arc length of the graph of

Accepted Answer

A)  2 
B)    
C)    
D)    
E)    
A)  2 
B)    
C)    
D)    
E)

Question 19

Find the curvature for r(t) = $\langle$ 6 cos 2t + 19, 6 sin 2t, 5t$\rangle$at t =  $\pi$.

Accepted Answer

The answer of Find the curvature for r(t) = $\langle$...

Question 20

At what points does 4x2 + 25y2 = 100 have minimum curvature?

Accepted Answer

A)  (0, -4), (0, 4) 
B)  (-4, 0), (4, 0) 
C)  (-5, 0), (5, 0) 
D)  (0, -5), (0, 5) 
E)  (0, -2), (0, 2) 
A)  (0, -4), (0, 4) 
B)  (-4, 0), (4, 0) 
C)  (-5, 0), (5, 0) 
D)  (0, -5), (0, 5) 
E)  (0, -2), (0, 2)

Find the arc length of the graph of

If , find when t = 1.

Describe the graph of .

Where is continuous?

A particle travels along a curve given by r(t) = 7 cos 3t i - 7 sin 3t j + 2k. Find the distance traveled by the particle during the time interval seconds.

Find the domain of

An object in an elliptical orbit has and Find r_max.

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

Find the arc length of the graph of

Find the domain of and calculate .

At what point does have maximum curvature?

Given G = 6.67 * 10^-11m³/kg·s², find the radius of a circular orbit above a 10⁵⁰-kg mass, if the orbiting object has a speed of 51 m/s.

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

Find the arc length of the parametric curve

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

r(t) = 3t i + 6t j + 7t k is the position vector of a particle moving in a plane. Find the acceleration of the particle.

If find

Find the arc length of the graph of

Find the curvature for r(t) = $\langle$ 6 cos 2t + 19, 6 sin 2t, 5t $\rangle$ at t = $\pi$ .

At what points does 4x² + 25y² = 100 have minimum curvature?

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

Find the arc length of the graph of

If , find when t = 1.

Describe the graph of .

Where is continuous?

A particle travels along a curve given by r(t) = 7 cos 3t i - 7 sin 3t j + 2k. Find the distance traveled by the particle during the time interval seconds.

Find the domain of

An object in an elliptical orbit has and Find rmax.

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

Find the arc length of the graph of

Find the domain of and calculate .

At what point does have maximum curvature?

Given G = 6.67 * 10-11 m3/kg·s2, find the radius of a circular orbit above a 1050-kg mass, if the orbiting object has a speed of 51 m/s.

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

Find the arc length of the parametric curve

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

r(t) = 3t i + 6t j + 7t k is the position vector of a particle moving in a plane. Find the acceleration of the particle.

If find

Find the arc length of the graph of

Find the curvature for r(t) = ⟨\langle⟨ 6 cos 2t + 19, 6 sin 2t, 5t ⟩\rangle⟩ at t = π\piπ .

At what points does 4x2 + 25y2 = 100 have minimum curvature?

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

An object in an elliptical orbit has and Find r_max.

Given G = 6.67 * 10^-11m³/kg·s², find the radius of a circular orbit above a 10⁵⁰-kg mass, if the orbiting object has a speed of 51 m/s.

Find the curvature for r(t) = $\langle$ 6 cos 2t + 19, 6 sin 2t, 5t $\rangle$ at t = $\pi$ .

At what points does 4x² + 25y² = 100 have minimum curvature?