Calculus II Chapter 10 Review
---------------------1. Sketch the curve represented by the parametric equations, and write the corresponding
rectangular equation by eliminating the parameter.
x=.Ji
y=t-2
2. Sketch the curve represented by the parametric equations, and write the corresponding
rectangular equation by eliminating the parameter.
y =est+ 1
3. Sketch the curve represented by the parametric equations, and write the corresponding
rectangular equation by eliminating the parameter.
y
= 4lnt
4. Find dy.
dx
X
=iff
y=3-t
5. Find dy and d ~ if possible, and find the slope and concavity (if possible) at the point
dx
dx
2
corresponding to B = 7r
4
x
y
.
= -7cosB
= -7sinB
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6. Find the arc length of the curve on the given interval.
x=Ji, y=7t-6, O~t~2
7. Find the area of the surface generated by revolving the curve about the given axis.
(i) x-axis; (ii) y-axis
8. For the given point in polar coordinates, find the corresponding rectangular coordinates
for the point.
9. For the given point in rectangular coordinates, find two sets of polar coordinates for the
point for 0 ~ ~ 21C .
e
10. Convert the rectangular equation to polar form.
2x- y+ 1 = 0
11. Convert the polar equation to rectangular form.
r
= 4sinB
12. Find the points of intersection ofthe graphs ofthe equations.
e
r=2.4
r=2.4
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13. Find the length of the curve over the given interval.
r
= 10 + 10 sine' 0 s e s 27r
14. Find the area of the surface formed by revolving about the polar axis the following
curve over the given interval.
7r
2
r=6cosB, OsBs-
15. Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch
and identifY the graph. Use a graphing utility to confirm your results.
2
r=--5+cosB
16. Find a polar equation for the ellipse with its focus at the pole, eccentricity e =
directrix y = --4.
2
, and
3
17. Find a polar equation for the hyperbola with its focus at the pole, eccentricity e =
directrix y = -5.
18. Find a polar equation for the parabola with its focus at the pole and vertex ( 10, ~
19. Find a polar equation for the ellipse with its focus at the pole and vertices
(14,0), (56,tr).
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_i , and
3
1r) .
jAnswerKey
1. y
=x2 -
dy
d 2y
5. dx =-cote, dx 2 =
2, x 2:: 0
Exercises: 9,10
Section: 10.3
6.
-6
-4
In ( 1, 570 + 56.J786) -In 2 + 28.fi86
56
Exercises: 47,48,51
Section: 10.3
24
7 [ . (")
11 7[
7 . (1') -48
-4
5
'
Exercises: 71
Section: 10.3
8. (0,7)
Exercises: 1-6
Section: 10.4
-6
Exercises: 9,10
Section: 10.2
2. y = x 5 +1
6
Exercises: 11-16
Section: 10.4
4
1
Exercises: 15,16
Section: 10.2
3. y = lnx
-2
4
6
-4
-6
Exercises: 29-30
Section: 10.2
4. dy = -8ti
5
9. (6,~} (-6, 7:)
8 .Y
8
1
7[
• At e =-:slope of -1 and concave up
3
7sin e
4
10. r = - - - - sine- 2cose
Exercises: 31
Section: 10.4
11. x 2 + (y- 2) 2 = 4
Exercises: 37
Section: 10.4
12. A and B
Exercises: 23
Section: 10.5
13. 80
Exercises: 47,48
Section: 10.5
14. 36n
Exercises: 55,56
Section: 10.5
. .
1
15. Eccentnc1ty: 5
Distance from pole to directrix: 2
The graph is an ellipse.
4
.Y
3
2
X
-4 -3 -2 -1-1
-2
-3
-4
Exercises: 14,15
Section: 10.6
8
16. r = - - 3- 2sine
Exercises: 35,36
Section: 10.6
20
17. r = - - - 3-4sine
Exercises: 37,38
Section: 10.6
20
18. r = - - 1 +sine
Exercises: 39,40
Section: 10.6
112
19. r = - - - 5 +3cose
Exercises: 41,42
Section: 10.6
dx
Exercises: 1,2
Section: 10.3
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