Pre-Calc Homework Solutions 238

Pre-Calc Homework Solutions 238 - 238 Section 6.1 d 2 x (x...

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Unformatted text preview: 238 Section 6.1 d 2 x (x e ) dx dx d (x sin x) dx dx 49. continued (b) Again, y x2 2 1 x 52. (a) C. 1 (b) (c) (d) f (x) dx g(x) dx [ f (x)] dx [ g(x)] dx [ f (x) x 2e x C C C C Initial condition: y( 1) 1 1 3 2 ( 1)2 1 2 ( 1) 1 C 2 x sin x x 2e x x sin x C f (x) dx g(x) dx f (x) dx x 2e x C x2 2 dy dx 1 x d 1 dx x 1 x2 3 ,x 2 x2 2 Solution: y (c) For x 0, 0 C1 (e) g(x)] dx g(x) dx C x sin x x (f) [ f (x) g(x)] dx f (x) dx x 2e x g(x) dx C x2 2 1 . x2 dy x2 d 1 For x 0, C2 dx 2 dx x 1 x x2 1 x . x2 dy And for x 0, is undefined. dx x x sin x f (x) dx 4 dx (g) (h) 53. (a) [x [g(x) f (x)] dx 4] dx k dt C1 x dx g(x) dx x 2e x 4x C C x sin x (d) Let C1 be the value from part (b), and let C2 be the value from part (a). Thus, C1 (e) y(2) 1 1 7 2 1 2 5 2 3 and C2 2 1 . 2 d 2s dt dt 2 ds kt dt Initial condition: 88 ( k)(0) C1 ds dt ds dt 88 when t 0 1 22 2 y( 2) C2 2 2 1 2 1 and C2 2 7 . 2 2 ( 2)2 1 2 ( 2) 3 C1 2 C1 88 C1 Velocity: ds dt dt kt 88 C2 ( kt k 2 t 2 k 2 (0) 2 88) dt C2 0 when t C2 0 C2 C1 s 88t Thus, C1 50. r dr dx dx Initial condition: s 0 0 88(0) (3x 3x 2 2 6x 12x 12) dx C 0 C (b) x 3 C2 kt 2 2 Initial condition: r(0) 0 0 03 C x3 3(0)2 12(0) Solution: s ds dt 88t 0 0 88 k 88 k 88 88 k 3872 k Solution: r(x) 51. c dc dx dx 3x 2 kt 12x 88 t (3x 2 6x 2 12x 15x C 15) dx (c) k 88 2 2 k x3 s 242 242 242 16 ft/sec 2 Initial condition c(0) 400 400 03 C x3 6(0)2 400 15(0) C k 6x 2 15x 400 Solution: c(x) ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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