Stewart – Calculus ET 8e Chapter 13 Form D
Select the correct answer for each question.
____ 1. Find the limit .
a.
b.
c.
d.
____ 2. Find a vector function that represents the curve of intersection of the two surfaces:
the top half of the ellipsoid and the parabolic cylinder .
a.
b.
c.
d.
e.
____ 3. If , find .
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form D
____ 4. Find the integral
a.
b.
c.
d.
____ 5. Find satisfying the conditions for
a.
b.
c.
d.
____ 6. If , evaluate .
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form D
____ 7. Find for the function given.
a.
b.
c.
d.
e.
____ 8. Reparametrize the curve with respect to arc length measured from the point where in the
direction of increasing .
a.
b.
c.
d.
e.
____ 9. Find the length of the curve
a.
36
b.
6
c.
26
d.
66
Stewart – Calculus ET 8e Chapter 13 Form D
____ 10. Find the length of the curve
a.
b.
c.
d.
____ 11. Find the curvature of the curve .
a.
4
3
b.
3
4
c.
51
16
d.
16
51
____ 12. Let C be a smooth curve defined by , and let and be the unit tangent
vector and unit normal vector to C corresponding to t. The plane determined by T and N is called
the osculating plane. Find an equation of the osculating plane of the curve described by at
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 13 Form D
____ 13. The torsion of a curve defined by is given by
Find the torsion of the curve defined by .
a.
27
29
b.
10
29
c.
50
29
d.
7
29
____ 14. At what point on the curve is the normal plane parallel to the plane
?
a.
b.
c.
d.
e.
____ 15. A particle moves with position function .
Find the tangential component of the acceleration vector.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form D
____ 16. Find the scalar tangential and normal components of acceleration of a particle with position vector
a.
b.
c.
d.
____ 17. Find the scalar tangential and normal components of acceleration of a particle with position vector
a. ,
b. ,
c. ,
d. ,
____ 18. What force is required so that a particle of mass has the following position function?.
a.
b.
c.
d.
e.
____ 19. Find the speed of a particle with the given position function.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form D
____ 20. A ball is thrown at an angle of to the ground. If the ball lands m away, what was the initial
speed of the ball? Let .
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form D
Answer Key
Stewart – Calculus ET 8e Chapter 13 Form E
____ 1. Find the domain of the vector function .
Select the correct answer.
a.
b.
c.
d.
____ 2. Find the limit .
Select the correct answer.
a.
b.
c.
d.
3. The helix intersects the curve at the point
. Find the angle of intersection.
4. Evaluate the integral.
____ 5. Find the unit tangent vector for at
Select the correct answer.
a.
3
121
i
3
121
j
7
242
k
b.
6
11
i +
6
11
j +
7
11
k
c.
d.
Stewart – Calculus ET 8e Chapter 13 Form E
____ 6. Find the integral
Select the correct answer.
a.
b.
c.
d.
7. If , evaluate .
8. Find parametric equations for the tangent line to the curve with the given parametric equations at
the specified point.
9. Find
for the function given.
10. Find parametric equations for the tangent line to the curve with the given parametric equations at
the specified point.
11. Find the curvature of .
____ 12. Find the length of the curve
Select the correct answer.
a.
36
b.
6
c.
26
d.
66
Stewart – Calculus ET 8e Chapter 13 Form E
____ 13. Find the length of the curve
Select the correct answer.
a.
b.
c.
d.
14. The torsion of a curve defined by is given by
Find the torsion of the curve defined by .
____ 15. The curvature of the curve given by the vector function is
Use the formula to find the curvature of at the point .
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form E
16. A particle moves with position function .
Find the tangential component of the acceleration vector.
17. Find the acceleration of a particle with the following position function.
18. Find the acceleration of a particle with the given position function.
____ 19. Find the scalar tangential and normal components of acceleration of a particle with position vector
Select the correct answer.
a.
b.
c.
d.
20. Find the speed of a particle with the given position function.
Stewart – Calculus ET 8e Chapter 13 Form E
Answer Key
Stewart – Calculus ET 8e Chapter 13 Form F
1. Let .
Find the domain of .
____ 2. Find the domain of the vector function .
Select the correct answer.
a.
b.
c.
d.
3. Find a vector function that represents the curve of intersection of the two surfaces:
the top half of the ellipsoid and the parabolic cylinder .
4. The helix intersects the curve at the point
. Find the angle of intersection.
5. Evaluate the integral.
6. If , evaluate .
____ 7. Find parametric equations for the tangent line to the curve with the given parametric equations at
the specified point. Select the correct answer.
a.
b.
c.
d.
e.