Question 1

Find the curvature   for

Accepted Answer

A)  1 
B)    
C)  0 
D)  sin2t - cos2t 
E)  - sin2t + cos2t 
A)  1 
B)    
C)  0 
D)  sin2t - cos2t 
E)  - sin2t + cos2t

Question 2

Sketch   . Calculate the radius of curvature at x = 1 and sketch the oscillating circle.

Accepted Answer

The answer of Sketch   . Calculate the radius...

Question 3

Find the domain of   and calculate   .

Accepted Answer

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

Question 4

A 2.03* 1030-kg object is orbited by an object 1.42 *1015 m above its center. If the orbit is circular, find its velocity. G = 6.67 * 10-11 m3/kg·s2.

Accepted Answer

The answer of A 2.03* 1030-kg object is orbited by...

Question 5

Let r(t) = e t i + e2t j + (e3t + 3)k. Find T(t) when t = 0.

Accepted Answer

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

Question 6

Find the arc length of the graph of

Accepted Answer

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

Question 7

If, for an elliptical orbit with semimajor axis a, rmin = a(1 - e) and rmax = a(1 + e), find the eccentricity if rmax = 1,100,000,000 km and rmin = 910,000,000 km.

Accepted Answer

Question 8

Find the domain of

Accepted Answer

The answer of Find the domain of  ...

Question 9

Find the curvature   for   .

Accepted Answer

A)    
B)    
C)    
D)  6 
E)    
A)    
B)    
C)    
D)  6 
E)

Question 10

Let r(t) = (t2 + 2)i + (e t + 4)j + e t k. Find N(t) for t = 0. Approximate your calculations to three decimal places.

Accepted Answer

A)  0 
B)  i 
C)  0.577j + 0.577k 
D)  i + 0.577j + 0.577k 
E)  i - 1.732j - 1.732k 
A)  0 
B)  i 
C)  0.577j + 0.577k 
D)  i + 0.577j + 0.577k 
E)  i - 1.732j - 1.732k

Question 11

Find the curvature for x = e t , y = 3 + e t cos t, z = e t sin t at t = 0.

Accepted Answer

Question 12

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 13

Let r(t) = e t i + (t + 2) j + 10 k. Find T(t) for t = 0.

Accepted Answer

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

Question 14

Find the radius of curvature for x = t2 + 4, y = t - 2, at t = 2.

Accepted Answer

Question 15

A particle travels along a curve given by r(t) = e t cos t i + e t sin t j + 12k. Find the distance traveled by the particle during the time interval 0 $\le$ t $\le$  $\pi$ seconds.

Accepted Answer

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

Question 16

If an asteroid has an orbit with eccentricity 0.59 and semi-major axis a = 130000000, find its minimum distance from the center of the sun.

Accepted Answer

r_min = a(1 - e) = 130,

Question 17

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 18

If   find

Accepted Answer

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

Question 19

If   find

Accepted Answer

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

Question 20

An object in orbit has rmax = 1024km and e = 0.27. Find rmin.

Accepted Answer

A)  5.75 * 1023km 
B)  6.32 *1023km 
C)  5.46 *1023km 
D)  5.75 *1026km 
E)  6.32 * 1026km 
A)  5.75 * 1023km 
B)  6.32 *1023km 
C)  5.46 *1023km 
D)  5.75 *1026km 
E)  6.32 * 1026km

Find the curvature for

Sketch . Calculate the radius of curvature at x = 1 and sketch the oscillating circle.

Find the domain of and calculate .

A 2.03* 10³⁰-kg object is orbited by an object 1.42 10¹⁵m above its center. If the orbit is circular, find its velocity. G = 6.67 10^-11 m³/kg·s².

Let r(t) = e ^t i + e²^t j + (e³^t + 3)k. Find T(t) when t = 0.

Find the arc length of the graph of

If, for an elliptical orbit with semimajor axis a, r_min = a(1 - e) and r_max = a(1 + e), find the eccentricity if r_max = 1,100,000,000 km and r_min = 910,000,000 km.

Find the domain of

Find the curvature for .

Let r(t) = (t² + 2)i + (e ^t + 4)j + e ^t k. Find N(t) for t = 0. Approximate your calculations to three decimal places.

Find the curvature for x = e ^t , y = 3 + e ^t cos t, z = e ^t sin t at t = 0.

Describe the graph of .

Let r(t) = e ^ti + (t + 2) j + 10 k. Find T(t) for t = 0.

Find the radius of curvature for x = t² + 4, y = t - 2, at t = 2.

A particle travels along a curve given by r(t) = e ^t cos t i + e ^t sin t j + 12k. Find the distance traveled by the particle during the time interval 0 $\le$ t $\le$ $\pi$ seconds.

If an asteroid has an orbit with eccentricity 0.59 and semi-major axis a = 130000000, find its minimum distance from the center of the sun.

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

If find

If find

An object in orbit has r_max = 10²⁴km and e = 0.27. Find r_min.

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 curvature for

Sketch . Calculate the radius of curvature at x = 1 and sketch the oscillating circle.

Find the domain of and calculate .

A 2.03* 1030-kg object is orbited by an object 1.42 *1015 m above its center. If the orbit is circular, find its velocity. G = 6.67 * 10-11 m3/kg·s2.

Let r(t) = e t i + e2t j + (e3t + 3)k. Find T(t) when t = 0.

Find the arc length of the graph of

If, for an elliptical orbit with semimajor axis a, rmin = a(1 - e) and rmax = a(1 + e), find the eccentricity if rmax = 1,100,000,000 km and rmin = 910,000,000 km.

Find the domain of

Find the curvature for .

Let r(t) = (t2 + 2)i + (e t + 4)j + e t k. Find N(t) for t = 0. Approximate your calculations to three decimal places.

Find the curvature for x = e t , y = 3 + e t cos t, z = e t sin t at t = 0.

Describe the graph of .

Let r(t) = e t i + (t + 2) j + 10 k. Find T(t) for t = 0.

Find the radius of curvature for x = t2 + 4, y = t - 2, at t = 2.

A particle travels along a curve given by r(t) = e t cos t i + e t sin t j + 12k. Find the distance traveled by the particle during the time interval 0 ≤\le≤ t ≤\le≤ π\piπ seconds.

If an asteroid has an orbit with eccentricity 0.59 and semi-major axis a = 130000000, find its minimum distance from the center of the sun.

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

If find

If find

An object in orbit has rmax = 1024km and e = 0.27. Find rmin.

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

A 2.03* 10³⁰-kg object is orbited by an object 1.42 10¹⁵m above its center. If the orbit is circular, find its velocity. G = 6.67 10^-11 m³/kg·s².

Let r(t) = e ^t i + e²^t j + (e³^t + 3)k. Find T(t) when t = 0.

If, for an elliptical orbit with semimajor axis a, r_min = a(1 - e) and r_max = a(1 + e), find the eccentricity if r_max = 1,100,000,000 km and r_min = 910,000,000 km.

Let r(t) = (t² + 2)i + (e ^t + 4)j + e ^t k. Find N(t) for t = 0. Approximate your calculations to three decimal places.

Find the curvature for x = e ^t , y = 3 + e ^t cos t, z = e ^t sin t at t = 0.

Let r(t) = e ^ti + (t + 2) j + 10 k. Find T(t) for t = 0.

Find the radius of curvature for x = t² + 4, y = t - 2, at t = 2.

A particle travels along a curve given by r(t) = e ^t cos t i + e ^t sin t j + 12k. Find the distance traveled by the particle during the time interval 0 $\le$ t $\le$ $\pi$ seconds.

An object in orbit has r_max = 10²⁴km and e = 0.27. Find r_min.