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A particle moves in the yz-plane along the curve represented by the vector-valued function A particle moves in the yz-plane along the curve represented by the vector-valued function .Find the minimum value of . ​ A) 6 B) 4 C) 7 D) 9 E) 8 .Find the minimum value of A particle moves in the yz-plane along the curve represented by the vector-valued function .Find the minimum value of . ​ A) 6 B) 4 C) 7 D) 9 E) 8 . ​


A) 6
B) 4
C) 7
D) 9
E) 8

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Determine the interval on which the vector-valued function Determine the interval on which the vector-valued function is continuous. ​ A) (9,∞) B) (5,∞) C) [5,∞) D) [9,∞) E) (-5,∞) is continuous. ​


A) (9,∞)
B) (5,∞)
C) [5,∞)
D) [9,∞)
E) (-5,∞)

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Uranus moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 2,876,769,540 kilometers,and the eccentricity is 0.0444.Find the minimum distance (perihelion) of Uranus from the sun.Round your answer to nearest kilometer. ​


A) 3,004,498,108 km
B) 2,749,040,972 km
C) 2,819,234,149 km
D) 7,819,870,365 km
E) 2,934,304,931 km

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Find the area of the inner loop of Find the area of the inner loop of . ​ A) B) C) D) E) . ​


A) Find the area of the inner loop of . ​ A) B) C) D) E)
B) Find the area of the inner loop of . ​ A) B) C) D) E)
C) Find the area of the inner loop of . ​ A) B) C) D) E)
D) Find the area of the inner loop of . ​ A) B) C) D) E)
E) Find the area of the inner loop of . ​ A) B) C) D) E)

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Find Find . ​ ​ A) B) C) D) E) . ​ Find . ​ ​ A) B) C) D) E) ​


A) Find . ​ ​ A) B) C) D) E)
B) Find . ​ ​ A) B) C) D) E)
C) Find . ​ ​ A) B) C) D) E)
D) Find . ​ ​ A) B) C) D) E)
E) Find . ​ ​ A) B) C) D) E)

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Find the second derivative Find the second derivative of the parametric equations , . ​ A) B) C) D) E) of the parametric equations Find the second derivative of the parametric equations , . ​ A) B) C) D) E) , Find the second derivative of the parametric equations , . ​ A) B) C) D) E) . ​


A) Find the second derivative of the parametric equations , . ​ A) B) C) D) E)
B) Find the second derivative of the parametric equations , . ​ A) B) C) D) E)
C) Find the second derivative of the parametric equations , . ​ A) B) C) D) E)
D) Find the second derivative of the parametric equations , . ​ A) B) C) D) E)
E) Find the second derivative of the parametric equations , . ​ A) B) C) D) E)

Correct Answer

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Find r' (t) given the following vector function. ​ Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
B) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
C) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
D) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
E) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​

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​A particle moves in the xy-plane such that its position for time ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​ is given by ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​ and ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​ .What is the slope of the tangent to the path of the particle when ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​ ? ​


A) ​ ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​
B) ​ ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​
C) ​ ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​
D) ​ ​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​ A) ​ B) ​ C) ​ D) ​

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Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above ​


A) Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above
Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above
B) Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above ​
Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above
C) Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above ​
Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above
D) Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above ​
Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​ A) B) ​ C) ​ D) ​ E) none of the above
E) none of the above

Correct Answer

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​The position vector of a particle moving in the xy-plane is ​The position vector of a particle moving in the xy-plane is for .For what value of y does the path of the particle have a horizontal tangent? ​ A) ​-300 B) ​ C) ​25 D) ​300 for ​The position vector of a particle moving in the xy-plane is for .For what value of y does the path of the particle have a horizontal tangent? ​ A) ​-300 B) ​ C) ​25 D) ​300 .For what value of y does the path of the particle have a horizontal tangent? ​


A) ​-300
B) ​ ​The position vector of a particle moving in the xy-plane is for .For what value of y does the path of the particle have a horizontal tangent? ​ A) ​-300 B) ​ C) ​25 D) ​300
C) ​25
D) ​300

Correct Answer

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Find Find . ​ ​ A) B) C) D) E) . ​ Find . ​ ​ A) B) C) D) E) ​


A) Find . ​ ​ A) B) C) D) E)
B) Find . ​ ​ A) B) C) D) E)
C) Find . ​ ​ A) B) C) D) E)
D) Find . ​ ​ A) B) C) D) E)
E) Find . ​ ​ A) B) C) D) E)

Correct Answer

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Match the equation with its graph. ​ Match the equation with its graph. ​ ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​ ​ ​


A) ​ ​
Match the equation with its graph. ​ ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​ ​
B) ​
Match the equation with its graph. ​ ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​ ​
C) ​
Match the equation with its graph. ​ ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​ ​
D) ​
Match the equation with its graph. ​ ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​ ​
E) ​ ​
Match the equation with its graph. ​ ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​ ​

Correct Answer

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​A particle moves in the xy​-plane so that its velocity vector for time ​A particle moves in the xy​-plane so that its velocity vector for time is .Which one of the following statements is true about the particle when ? ​ A) ​The particle is speeding up. B) ​​The particle is slowing down. C) ​​The particle is at rest. D) ​​The speed of the particle is . is ​A particle moves in the xy​-plane so that its velocity vector for time is .Which one of the following statements is true about the particle when ? ​ A) ​The particle is speeding up. B) ​​The particle is slowing down. C) ​​The particle is at rest. D) ​​The speed of the particle is . .Which one of the following statements is true about the particle when ​A particle moves in the xy​-plane so that its velocity vector for time is .Which one of the following statements is true about the particle when ? ​ A) ​The particle is speeding up. B) ​​The particle is slowing down. C) ​​The particle is at rest. D) ​​The speed of the particle is . ? ​


A) ​The particle is speeding up.
B) ​​The particle is slowing down.
C) ​​The particle is at rest.
D) ​​The speed of the particle is ​A particle moves in the xy​-plane so that its velocity vector for time is .Which one of the following statements is true about the particle when ? ​ A) ​The particle is speeding up. B) ​​The particle is slowing down. C) ​​The particle is at rest. D) ​​The speed of the particle is . .

Correct Answer

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Find the arc length of the curve on the given interval. ​ Find the arc length of the curve on the given interval. ​ A) B) C) D) E)


A) Find the arc length of the curve on the given interval. ​ A) B) C) D) E)
B) Find the arc length of the curve on the given interval. ​ A) B) C) D) E)
C) Find the arc length of the curve on the given interval. ​ A) B) C) D) E)
D) Find the arc length of the curve on the given interval. ​ A) B) C) D) E)
E) Find the arc length of the curve on the given interval. ​ A) B) C) D) E)

Correct Answer

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Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​ Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​ ​ A) parabola B) ellipse C) circle D) hyperbola ​


A) parabola
B) ellipse
C) circle
D) hyperbola

Correct Answer

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Find Find given the following vector function. ​ ​ A) B) C) D) E) given the following vector function. ​ Find given the following vector function. ​ ​ A) B) C) D) E) ​


A) Find given the following vector function. ​ ​ A) B) C) D) E)
B) Find given the following vector function. ​ ​ A) B) C) D) E)
C) Find given the following vector function. ​ ​ A) B) C) D) E)
D) Find given the following vector function. ​ ​ A) B) C) D) E)
E) Find given the following vector function. ​ ​ A) B) C) D) E)

Correct Answer

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Match the equation with the graph shown in red below. ​ Match the equation with the graph shown in red below. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) Match the equation with the graph shown in red below. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
B) Match the equation with the graph shown in red below. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
C) Match the equation with the graph shown in red below. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
D) Match the equation with the graph shown in red below. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
E) Match the equation with the graph shown in red below. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​

Correct Answer

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Find the length of the curve over the given interval. Find the length of the curve over the given interval. A) B) C) D) E)


A) Find the length of the curve over the given interval. A) B) C) D) E)
B) Find the length of the curve over the given interval. A) B) C) D) E)
C) Find the length of the curve over the given interval. A) B) C) D) E)
D) Find the length of the curve over the given interval. A) B) C) D) E)
E) Find the length of the curve over the given interval. A) B) C) D) E)

Correct Answer

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Use the given acceleration function and initial conditions to find the position at time Use the given acceleration function and initial conditions to find the position at time . ​ ​ A) B) C) D) E) . ​ Use the given acceleration function and initial conditions to find the position at time . ​ ​ A) B) C) D) E) ​


A) Use the given acceleration function and initial conditions to find the position at time . ​ ​ A) B) C) D) E)
B) Use the given acceleration function and initial conditions to find the position at time . ​ ​ A) B) C) D) E)
C) Use the given acceleration function and initial conditions to find the position at time . ​ ​ A) B) C) D) E)
D) Use the given acceleration function and initial conditions to find the position at time . ​ ​ A) B) C) D) E)
E) Use the given acceleration function and initial conditions to find the position at time . ​ ​ A) B) C) D) E)

Correct Answer

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Find r' (t) given the following vector function. ​ Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
B) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
C) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
D) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
E) Find r' (t) given the following vector function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​

Correct Answer

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