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35.32 (a) 1 1 3 ; (b) ln (e + 1) ln 2; (c) 1 2 . 2 2 e 35.33 e 1.
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35.35 (b) Approximately 11.55 years; (c) after 1 year, 1 dollar yields: (i) 1.05 dollars when compounded once a year; (ii) about 1.05116 dollars when compounded monthly; (iii) about 1.0512 dollars when compounded continuously. 35.36 (a) 0.5671432904; (b) 1.309799586. 35.37 0.8556513176.
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1 36.9 (a) + ; (b) 1; (c) 0; (d) 0; (e) 1; ( f ) + ; (g) 1; (h) ; (i) 1; ( j) 1; (k) ln 3 ln 2; (l) + ; (m) 0; (n) 1; (o) 0; (p) e3 ; 2 1 3 (q) + ; (r) 0; (s) 1/ ; (t) ; (u) 3; (v) 4; (w) . 7 2 36.10 See Fig. A-28. 36.11 8 times.
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36.12 1690
ln 10 1690(3.32) 5611 years. ln 2
36.13 e (12 ln 2)/23 0.7 g.
36.14 T =
0.6931 ln 2 3.1 years. ln 10 3 ln 2 2.3026 2.0793 36.18 288 billion. 36.19 (a) 800; (b)
36.15 69.31 days. 375 541. ln 2
36.16 3.125 g.
36.17 72 900.
37.12 (a) f 1 ( y) = 2y 6; (c) f 1 ( y) = (h) f 1 ( y) =
5 + 2y 1 5 ; (e) f 1 ( y) = 5 y + 1; ( f ) f 1 ( y) = = f ( y); (g) f 1 ( y) = ; 3+y y y 3 1 y+2 4; (i) f 1 ( y) = . y y 1
37.13 (a)
7 5 3 4 5 ; (b) ; (c) ; (d) ; (e) ; ( f ) ; (g) ; (h) ; (i) . 6 4 4 6 4 6 4 4 3
37.14 (a) sin =
3 2 2 2 2 , tan = 2 2, cot = , sec = 3, csc = ; 3 4 4 4 15 15 15 , tan = , cot = 15, sec = , csc = 4. (b) cos = 4 15 15
12 2 2 5 3 37.15 (a) ; (b) ; (c) (2 3 2); (d) ( 6 1); (e) 0. 5 5 15 25 37.16 Domain = ( , ), range = (0, 1]. 37.17 (a) sin 1 x + cos 1 x = (d) tan 1 x + tan 1 5 /2 ; (b) tan 1 x + cot 1 x = ; (c) sec 1 x + csc 1 x = 2 2 /2 or cot 1 x = tan 1 1 . x for x 1 for x 1
1 = x 2
37.18 (a)
x 1 1 3 sin x ; (e) ex cos 1 x ; ; (c) + tan 1 x; (b) ; (d) 1 + x2 1 + cos2 x (1 + 9x 2 ) cot 1 3x (2 x) 1 x 1 x2 1 2 a2 x 2 if x > 0 if a > 0 1 1 x2 2 1 x (f) ; (g) ; (i) ; (h) = ; 2x 2 1 x)(1 + x 2 ) 1 2 if a < 0 1 + x2 (tan x 1 x if x < 0 2 x2 a 1 x2 if x > 0 0 2 2 ( j) if x < 0 ; (k) x 2 + 4 . x x2 1 u+v . 1 uv
37.19 tan 1 u + tan 1 v = tan 1
37.20 (a)
x 3x x 4x 1 1 1 tan 1 + C; (b) tan 1 + C; (c) sin 1 + C; (d) sin 1 + C; (e) sec 1 (x 3) + C; 2 2 6 2 4 5 5 1 6x 14x x 3x 1 1 1 + C; (g) tan 1 + C; (h) sec 1 + C; (i) sec 1 + C; ( f ) sin 1 3 2 2 2 4 4 2 14
ANS.]
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