Stewart – Calculus ET 8e Chapter 13 Form F
8. Reparametrize the curve with respect to arc length measured from the point where in the
direction of increasing .
9. For the curve given by , find the unit normal vector.
____ 10. Find the length of the curve
Select the correct answer.
a.
25
b.
45
c.
26
d.
6
____ 11. Find the length of the curve
Select the correct answer.
a.
b.
c.
d.
12. The torsion of a curve defined by is given by
Find the torsion of the curve defined by .
____ 13. Use Simpson’s Rule with n = 4 to estimate the length of the arc of the curve with equations
, from to . Round your answer to four decimal places.
Select the correct answer.
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 13 Form F
____ 14. At what point on the curve is the normal plane parallel to the plane
?
Select the correct answer.
a.
b.
c.
d.
e.
15. Find the velocity of a particle that has the given acceleration and the given initial velocity.
16. Find the scalar tangential and normal components of acceleration of a particle with position vector
17. What force is required so that a particle of mass has the following position function?.
____ 18. A projectile is fired with an initial speed of and angle of elevation . Find the range of
the projectile. Select the correct answer.
a. km
b. km
c. km
d. km
e. km
19. 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 .
Stewart – Calculus ET 8e Chapter 13 Form F
____ 20. The following table gives coordinates of a particle moving through space along a smooth curve.
Find the average velocity over the time interval . Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form F
Answer Key
Stewart – Calculus ET 8e Chapter 13 Form G
1. Find the limit.
____ 2. Find the domain of the vector function .
Select the correct answer.
a.
b.
c.
d.
____ 3. Find the limit .
Select the correct answer.
a.
b.
c.
d.
4. Find a vector function that represents the curve of intersection of the two surfaces:
the top half of the ellipsoid and the parabolic cylinder .
____ 5. If , find .
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 13 Form G
6. The helix intersects the curve at the
point . Find the angle of intersection.
7. Find the unit tangent vector for at
____ 8. Find parametric equations for the tangent line to the curve with parametric equations
at the point with Select the correct answer.
a.
b.
c.
d.
9. If , evaluate .
____ 10. 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.
11. Find
for the function given.
12. Find parametric equations for the tangent line to the curve with the given parametric equations at
the specified point.
13. Find the unit tangent vector for the curve given by .
Stewart – Calculus ET 8e Chapter 13 Form G
____ 14. Find the length of the curve Select the correct answer.
a.
b.
c.
d.
____ 15. Find the curvature of the curve . Select the correct answer.
a.
62
b. 0
c. 9
d. 1
____ 16. Find the curvature of the curve . Select the correct answer.
a.
7
2
b.
2
7
c.
49
100
d.
100
49
17. 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
Stewart – Calculus ET 8e Chapter 13 Form G
____ 18. A particle moves with position function .
Find the tangential component of the acceleration vector. Select the correct answer.
a.
b.
c.
d.
e.
____ 19. Find the velocity of a particle that has the given acceleration and the given initial velocity.
Select the correct answer.
a.
b.
c.
d.
e.
20. Find the speed of a particle with the given position function.
Stewart – Calculus ET 8e Chapter 13 Form G
Answer Key
Stewart – Calculus ET 8e Chapter 13 Form H
1. Find the limit.
____ 2. Find the domain of the vector function .
Select the correct answer.
a.
b.
c.
d.
____ 3. Find the limit .
Select the correct answer.
a.
b.
c.
d.
4. Find the unit tangent vector .
5. Find parametric equations for the tangent line to the curve with the given parametric equations at
the specified point.
6. Find
for the function given.
7. Find the curvature of .
Stewart – Calculus ET 8e Chapter 13 Form H
____ 8. Find the length of the curve
Select the correct answer.
a.
b.
c.
d.
____ 9. Find the curvature of the curve .
Select the correct answer.
a. 1
b.
210
c. 11
d. 0
10. Find the curvature of the curve .
11. At what point on the curve is the normal plane parallel to the plane
?
12. A particle moves with position function .
Find the tangential component of the acceleration vector.
____ 13. A force with magnitude N acts directly upward from the xy-plane on an object with mass
kg. The object starts at the origin with initial velocity . Find its position function.
Select the correct answer.
a.
b.
c.
d.
e.
7
6
Stewart – Calculus ET 8e Chapter 13 Form H
____ 14. Find the acceleration of a particle with the following position function.
Select the correct answer.
a.
b.
c.
d.
e.
15. Find the speed of a particle with the given position function.
16. Find the velocity of a particle that has the given acceleration and the given initial velocity.
17. The position function of a particle is given by
When is the speed a minimum?
____ 18. A mortar shell is fired with a muzzle speed of 325 ft/sec. Find the angle of elevation of the mortar
if the shell strikes a target located 1500 ft away. Round your answer to 2 decimal places.
Select the correct answer.
a.
b.
c.
d.
19. A projectile is fired with an initial speed of and angle of elevation . Find the range of
the projectile.
20. Find the speed of a particle with the given position function.
Stewart – Calculus ET 8e Chapter 13 Form H
Answer Key