Pre-Calc Homework Solutions 353

Pre-Calc Homework Solutions 353 - Section 8.4 dx x 2 353...

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Unformatted text preview: Section 8.4 dx x 2 353 43. dy x x y 2 45. For x 9 0, y 3 0 on [0, 3] 9 3 x2 Area 3 sec 2 dx d ,0 9 cos 2 3 sec , dx 9 9 sec dx x2 9 3 sec tan 3 tan tan 9 tan d ,0 2 0 2 x 9 3 sin , dx x 2 3 cos 2 9 2 9 0, x 3 2 9 sin When x d 3 0 0 and when x /2 0 0 3, d 2 . 9 dx /2 3 cos 3 3 cos d sec ln sec ln x 3 d tan x2 3 9 3 cos2 1 /2 0 3 C 3 C ln 3. 46. Volume C or C 0 x The solution to the initial value problem is y 44. (x 2 0 2 3 4 1 cos 2 d 2 /2 sin 2 4 0 2.356 2 1 Substitute x ln 3 5 ln 3 5, y 4 3 2 1 x 2 dx d ,0 sec 2 4 0 (1 dx x 2)2 tan , dx x2 1 0, sec 2 tan 2 4 (since 0 x 1) ln x 3 2 dy x2 3 9 1 . When x dx dx (x 2 1)3/2 0 and when x /4 0 /4 1, 1) x 2 1 4 . 1 0 dy x x2 y dx (1 x 2)2 sec 2 sec 4 d d tan , dx 1 tan 2 sec 2 1 d , sec 2 cos 2 1 2 2 0 /4 0 dx (x 2 1)3/2 2 sec d sec 3 1 2 8 1 4 1 4 cos 2 d 2 /4 sin 2 4 0 cos sin x x2 d Volume C C 1 4 8 2 1 8.076 47. (a) 1. Substitute x 1 C 0, y dx x(1000 1 x(1000 x) x) 1 dt 250 A B x 1000 x 1 A(1000 ( A x) B)x Bx 1000A The solution to the initial value problem is y x x2 1 1. Equating the coefficients and solving for A and B gives A 1 ,B 1000 dx x(1000 x) 1 1000 (1/1000) dx (1/1000) dx x 1000 x 1 1 ln x ln (1000 x) 1000 1000 1 x ln C1 1000 1000 x t C2 x 250 C1 1 x ln 1000 1000 x ln 4t C 1000 x x e 4t C Ae 4t 1000 x ...
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