James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

Stewart / Calculus: ET 5 th Editio n
Solution Ar t
Appendix I
5et040523
Answers to Odd-Numbered 5.20.02 Exercises A85
13. A. s2`, 22d ø s22, 2d ø s2, `d B. y-int 0; x-int 0
C. About s0, 0d D. VA x − 62; HA y − 0
E. Dec on s2`, 22d, s22, 2d, s2, `d y
F. No local extrema
G. CU on s22, 0d, s2, `d;
CD on s2`, 22d, s0, 2d; IP s0, 0d
H. See graph at right.
15. A. R B. y-int 0; x-int 0
C. About y-axis D. HA y − 1
E. Inc on s0, `d; dec on s2`, 0d
F. Loc min f s0d − 0
G. CU on s21, 1d;
5.20.02
CD on s2`, 21d, s1, `d; IPs s61, 1 4d
H. See graph at right.
17. A. s2`, 0d ø s0, `d B. x-int 1
C. None D. HA y − 0; VA x − 0
E. Inc on s0, 2d;
dec on s2`, 0d, s2, `d
F. Loc max f s2d − 1 4
G. CU on s3, `d;
CD on s2`, 0d, s0, 3d; IP s3, 2 9d
H. See graph at right.
x=_2
Stewart / Calculus: ET 5 th Editio n
Solution Ar t (0, 0)
5et040517
5.20.02
y
(0, 0)
x=2
y=1
Stewart / Calculus: ET 5 th Editio n
Solution Ar t
5et040515
1
”_1, ’
4
y
0 1
1
”1, ’
4
1
”2, ’
4
19. A. s2`, 21d ø s21, `d y
B. y-int 0; x-int 0 C. None
D. VA x − 21; HA y − 1
E. Inc on s2`, 21d, s21, `d;
Œ„„„ 1/2
F. None
G. CU on s2`, 21d, (0, s 3 1 2
);
(0, 0)
CD on s21, 0d, (s 3 1 2 , `);
IPs s0, 0d, (s 3 1 2 , 1 3
)
H. See graph at right.
21. A. f0, `d B. y-int 0; x-int 0, 3
C. None D. None
E. Inc on s1, `d; dec on s0, 1d
F. Loc min f s1d − 22
G. CU on s0, `d
H. See graph at right.
y
0
x=_1
(1, _2)
3
1
3
x
2
”3, ’
9
x
x
y=1
x
x
25. A. R B. y-int 0; x-int 0
C. About s0, 0d
D. HA y − 61
E. Inc on s2`, `d F. None
G. CU on s2`, 0d;
CD on s0, `d; IP s0, 0d
H. See graph at right.
y=1
y=_1
y
(0, 0)
27. A. f21, 0d ø s0, 1g B. x-int 61 C. About (0, 0)
D. VA x − 0
E. Dec on s21, 0d, s0, 1d
y
F. None
1
G. CU on (21, 2s2y3),
0 1
(0, s2y3);
CD on (2s2y3, 0), (s2y3, 1);
IPs (6s2y3, 61ys2 )
H. See graph at right.
Stewart / Calculus: ET 5 th Editio n
Solution Ar t
5et040527
5.20.02
29. A. R B. y-int 0; x-int 63s3, 0 C. About s0, 0d
D. None E. Inc on s2`, 21d, s1, `d; dec on s21, 1d
F. Loc max f s21d − 2;
y
loc min f s1d − 22
_1, 2
G. CU on s0, `d;
0, 0
CD on s2`, 0d; IP s0, 0d
0
H. See graph at right.
_3œ„3, 0
31. A. R B. y-int 21; x-int 61
C. About the y-axis D. None
E. Inc on s0, `d; dec on s2`, 0d
F. Loc min f s0d − 21
G. CU on s21, 1d;
CD on s2`, 21d, s1, `d; IPs s61, 0d
H. See graph at right.
33. A. R B. y-int 0; x-int n (n an integer)
C. About s0, 0d, period 2 D. None
E–G answers for 0 < x < :
1, _2
y
ms80344-1
6et 4.5.29
8.10.06
x
3œ„3, 0
(_1, 0) 0 (1, 0) x
(0, _1)
E. Inc on s0, y2d; dec on sy2, d F. Loc max f sy2d − 1
G. Let − sin 21 s2y3 ; CU on s0, d, s 2 , d;
CD on s, 2 d; IPs at x − 0, , , 2
H.
_2π
y
0
2π
x
x
4π
x
23. A. s2`, 22g ø f1, `d
B. x-int 22, 1 C. None
D. None
E. Inc on s1, `d; dec on s2`, 22d
F. None
G. CD on s2`, 22d, s1, `d
H. See graph at right.
_2
y
0 x 1
35. A. s2y2, y2d B. y-int 0; x-int 0 C. About y-axis
D. VA x − 6y2
y
E. Inc on s0, y2d;
dec on s2y2, 0d
F. Loc min f s0d − 0
x π 2 x π 2
G. CU on s2y2, y2d
H. See graph at right.
0
x
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ms80342-1