1. Find the following limit.
2. Find the point of intersection of the tangent lines to the curve , at the
points where and .
3. Find an expression for .
4. The curves and intersects at the origin. Find their angle of
...
1. Find the following limit.
2. Find the point of intersection of the tangent lines to the curve , at the
points where and .
3. Find an expression for .
4. The curves and intersects at the origin. Find their angle of
intersection correct to the nearest degree.
5. Find the derivative of the vector function.
6. Find if and .
7. Find equations of the normal plane to at the point (2, 4, 8).
8. A particle moves with position function . Find the acceleration of the
particle.
9. A particle moves with position function .
Find the normal component of the acceleration vector.
10. Find the position vector of a particle that has the given acceleration and the given initial velocity
and position.
11. Sketch the curve of the vector function and indicate the orientation
of the curve.
12. Sketch the curve of the vector function , and indicate the orientation of the
curve.Stewart - Calculus ET 8e Chapter 13 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
13. Sketch the curve of the vector function and indicate the orientation of the
curve.
14. Find the limit .
15. Sketch the curve of the vector function and indicate the orientation
of the curve.
16. Find the integral
17. Find the unit tangent and unit normal vectors and for the curve C defined by
Sketch the graph of C, and show and for
18. Find the velocity, acceleration, and speed of an object with position function
for Sketch the path of the object and its velocity and acceleration vectors.
19. Find the scalar tangential and normal components of acceleration of a particle with position vector
20. Find the velocity and position vectors of an object with acceleration
initial velocity and initial positionStewart - Calculus ET 8e Chapter 13 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
(–3, 5)
(6, 14)
–4 –3 –2 –1 1 2 3 4 5 6 7 8 x
9 8 7 6 5 4
10
11
12
13
14
15
yStewart - Calculus ET 8e Chapter 13 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
12.
–6 –4 –2 2 4 6 x
6 4 2
–2
–4
–6
y
13.
14.
15.
(–3, 1)
(6, 7)
–4 –3 –2 –1 1 2 3 4 5 6 7 8 x
9 8 7 6 5 4 3 2 1
10
11
12
y
16.Stewart - Calculus ET 8e Chapter 13 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
17. ,
T(1)
N(1)
–4 –3 –2 –1 1 2 3 4 x
9 8 7 6 5 4 3 2 1
–1
y
18. 34
acc. vel.
–6 –4 –2 2 4 6 x
6 4 2
–2
–4
–6
y
19. ,
20.Stewart - Calculus ET 8e Chapter 13 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. Find for the function given.
2. Find an expression for .
3. Find equations of the normal plane to at the point (2, 4, 8).
4. Sketch the curve of the vector function , and indicate the orientation of the
curve.
5. Sketch the curve of the vector function and indicate the orientation of the
curve.
6. Find the limit .
7. Sketch the curve of the vector function and indicate the orientation
of the curve.
8. Sketch the curve of the vector function , and indicate the orientation of the
curve.
9. Find a vector function describing the curve of intersection of the cylinder and the
plane
10. Find and for
11. Find and for
12. Find the integral
13. Find the derivative
14. Given
a. Find and .
b. Sketch the curve defined by r and the vectors and on the same set of axes.Stewart - Calculus ET 8e Chapter 13 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
15. Find the arc length function for the curve defined by for
Then use this result to find a parametrization of C in terms of s.
16. Find the velocity, acceleration, and speed of an object with position function
for Sketch the path of the object and its velocity and acceleration vectors.
17. A projectile is fired from a height of 350 ft with an initial speed of 200 ft/sec and an angle of
elevation of .
a. What are the scalar tangential and normal components of acceleration of the projectile?
b. What are the scalar tangential and normal components of acceleration of the projectile when the
projectile is at its maximum height?
18. Find the velocity, acceleration, and speed of an object with position vector .
19. Find the velocity, acceleration, and speed of an object with position vector .
20. Find the velocity and position vectors of an object with acceleration
initial velocity and initial positionStewart - Calculus ET 8e Chapter 13 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2.
3.
4.
–6 –4 –2 2 4 6 x
6 4 2
–2
–4
–6
y
5.
6.Stewart - Calculus ET 8e Chapter 13 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
7.
(–3, 1)
(6, 7)
–4 –3 –2 –1 1 2 3 4 5 6 7 8 x
9 8 7 6 5 4 3 2 1
10
11
12
y
8.
–6 –4 –2 2 4 6 x
6 4 2
–2
–4
–6
y
9.
10. ,
11. ,
12.
13.
14. ,Stewart - Calculus ET 8e Chapter 13 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
r(-1)
r'(-1)
–10 –8 –6 –4 –2 2 4 6 8 10 x
8 6 4 2
10
–2
–4
–6
–8
–10
y
15. ,
,
16. 13
a(1) v(1)
2 4 6 8 10 12 x
8 7 6 5 4 3 2 1
y
17. a. , b.
18.
19.
69
20.Stewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Select the correct answer for each question.
____ 1. Find the limit.
a.
b.
c.
d.
e.
____ 2. Let .
Find the domain of .
a.
b.
c.
d.
e.
____ 3. Find the domain of the vector function .
a.
b.
c.
d.Stewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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 .
a.
b.
c.
d.
e.
____ 5. Find a vector function that represents the curve of intersection of the two surfaces:
The circular cylinder and the parabolic cylinder .
a.
b.
c.
d.
e.
____ 6. If , find .
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. The helix intersects the curve at the point
. Find the angle of intersection.
a.
b.
c.
d.
e. None of these
____ 8. Find parametric equations for the tangent line to the curve with parametric equations
at the point with
a.
b.
c.
d.Stewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 9. Find the unit tangent vector for the curve given by .
a.
b.
c.
d.
e. None of theseStewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 10. Reparametrize the curve with respect to arc length measured from the point where in the
direction of increasing .
a.
b.
c.
d.
e.
____ 11. Find the length of the curve
a. 2 14
b. 14
c. 6 14
d. 3 14Stewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 12. The torsion of a curve defined by is given by
Find the torsion of the curve defined by .
a. 21
41
b. 9
41
c. 20
41
d. 80
41
____ 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.
a.
b.
c.
d.
e. None of theseStewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 14. The curvature of the curve given by the vector function is
Use the formula to find the curvature of at the point .
a.
b.
c.
d.
e.
____ 15. Find the velocity of a particle with the given position function.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 16. Find the speed of a particle with the given position function.
a.
b.
c.
d.
e.
____ 17. A mortar shell is fired with a muzzle speed of 250 ft/sec. Find the angle of elevation of the mortar
if the shell strikes a target located 1100 ft away. Round your answer to 2 decimal places.
a.
b.
c.
d.
____ 18. Find the scalar tangential and normal components of acceleration of a particle with position vector
a.
b.
c.
d.
____ 19. A projectile is fired with an initial speed of and angle of elevation . Find the range of
the projectile.
a. km
b. km
c. km
d. km
e. kmStewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 20. The following table gives coordinates of a particle moving through space along a smooth curve.
Find the average velocity over the time interval .
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 13 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. E
2. A
3. A
4. C
5. E
6. A
7. C
8. B
9. C
10. C
11. D
12. C
13. C
14. B
15. B
16. D
17. A
18. D
19. A
20. DStewart – Calculus ET 8e Chapter 13 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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. 3 6
b. 6
c. 2 6
d. 6 6Stewart – Calculus ET 8e Chapter 13 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. C
2. A
3. C
4. C
5. B
6. B
7. B
8. D
9. A
10. C
11. D
12. D
13. B
14. C
15. E
16. A
17. A
18. A
19. D
20. AStewart – Calculus ET 8e Chapter 13 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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 121 3 j 242 7 k
b. 6
11 i + 11 6 j + 11 7 k
c.
d.Stewart – Calculus ET 8e Chapter 13 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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. 3 6
b. 6
c. 2 6
d. 6 6Stewart – Calculus ET 8e Chapter 13 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. B
2. C
3.
4.
5. B
6. C
7.
8.
9.
10.
11.
12. A
13. C
14. 10
29
15. B
16.
17.
18.
19. A
20.Stewart - Calculus ET 8e Chapter 13 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.Stewart - Calculus ET 8e Chapter 13 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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. 2 5
b. 4 5
c. 2 6
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.
e. None of theseStewart - Calculus ET 8e Chapter 13 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2. A
3.
4.
5.
6.
7. C
8.
9.
10. B
11. B
12. 28
65
13. C
14. B
15.
16. ,
17.
18. D
19.
20. DStewart - Calculus ET 8e Chapter 13 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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. 6 2
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 atStewart - Calculus ET 8e Chapter 13 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2. B
3. C
4.
5. D
6.
7. 2
3 i + 1 3 j + 2 3 k
8. A
9.
10. C
11.
12.
13.
14. D
15. B
16. C
17.
18. B
19. D
20.Stewart - Calculus ET 8e Chapter 13 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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. 2 10
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
6Stewart - Calculus ET 8e Chapter 13 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 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
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Answer Key
1.
2. D
3. C
4.
5.
6.
7.
8. C
9. D
10. 16
51
11.
12.
13. E
14. A
15.
16.
17.
18. C
19. km
20.
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