Transcript Chapter 10.1

Chapter 10
Major theorems, figures, and student response questions
Calculus 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.1.3 (p. 693)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
10.1.1 (p. 698)
Arc Length Formula for Parametric Curves
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figures 10.1.14 and 10.1.15
(p. 699)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.2.1 (p. 706)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.2.5 (p. 706)
Equation (1)
Equation (2)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.2.13 (p. 710)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Theorem 10.2.1 (p. 710)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
10.3.2 (p. 722)
Arc Length Formula for Polar Curves
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
10.3.3 (p. 722)
10.3.4 (p. 723)
Area in Polar Coordinates
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.3.8 (p. 723)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.3.9 (p. 723)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Area in Polar Coordinates: Limits of Integration
(p. 723)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.4.1 (p. 730)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Definitions 11.4.1, 11.4.2, and 11.4.3 (p. 731)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.4.6 (p. 732)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Sketching a Parabola from Its Standard Equation
(p. 733)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.4.14 (p. 735)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Sketching an Ellipse from Its Standard Equation
(p. 736)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.4.22 (p. 738)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Sketching a Hyperbola from Its Standard Equation
(p. 739)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Equations (12) – (16) (p. 740)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Equations (17) – (19) (p. 740)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Theorems 10.4, 10.5, and 10.6 (pp. 742 – 743)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.5.2 (p. 749)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Theorem 10.5.1 (p. 750)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Theorem 10.6.1 (p. 754)
Figure 10.6.1 (p. 754)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Figure 10.6.3 (p. 755)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Theorem 10.6.2 (p. 756)
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
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


Select the best answer for the following question.
1. Find parametric equations for the semicircle of radius 3 in
quadrants II and III, oriented counterclockwise.
a) x  3cost, y  3sint,
0  t  2 
b) x  3cost, y  3sint,
2  t  32 
c) x  3cost, y  3sint,
2  t   
d) x  3cost, y  3sin t,
2  t  32 
Question 1
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Select the best answer for the following question.
2. Find dy dx at the given point without eliminating the
parameter. x  2t 3, y  8t 3  5t 2, t 1
 a) 1

b) 3
2
c) 7

3
d) 3

Question 2
7
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.



Select the best answer for the following question.
3. Find the rectangular coordinates of the point whose polar
coordinates are 5,  .
 3
5 3 
5
a) 
 2 ,  2 



5 3 5 
b) 
 2 , 2 


c) 
5 2 2 ,

d) 
52 ,

5 2 

2 
5 3 

2 
Question 3
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.



Select the best answer for the following question.
4. Find polar equations of the tangent line(s) to the curve at
the pole. r  2sin2
a)   0,   

b)    ,   3
2
2
c)    ,    ,   3
2
2
d)   0,    ,    ,   3
2
2
Question 4
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Select the best answer for the following question.
5. Write an expression for the area in the second quadrant
within the cardioid r  1 cos  .

a)

2


b)

2

1
2
1 cos  d
2
0

c)


 1 cos d
2
1
2
 1 cosd

2

d)
 1 cos d
Question 5
2

2
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.



Select the best answer for the following question.
6. Find the focus, vertex, and directrix of the parabola
y 2  2y  8x 1  0.
a) focus = 2,1 vertex= 0,1 directrix: x  2

b) focus = 2,1 vertex= 0,1 directrix: x  2
c) focus= 0, 1 vertex= 0,1 directrix: y = 3
d) focus = 0, 3 vertex= 0,1 directrix: y = -1Question 6
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.




Select the best answer for the following question.
7. Find the equation of the ellipse with ends of the major axis
at 1,  3 and ends of the minor axis at 0, 0, 2, 0.
x 1
2
a)
9
 y2 1

2
y
b) x  1 
1
9
2
2
y
c) x 1 
1
9
2
2
y
d) x 1 
1
3
2
Question 7
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Answers
1. b
6. b
2. c
7. c
3. d
4. d
5. a
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.