Pre-Calc Homework Solutions 354

Pre-Calc Homework Solutions 354 - 354 Section 8.4 x 2 sin x...

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Unformatted text preview: 354 Section 8.4 x 2 sin x . cos x 47. continued When t 2 998 x 1000 49. (a) From the figure, tan 0, x 2. 1 499 1 A or A (b) From part (a), z z(1 z 2(1 z 2(1 z 2(1 (1 1 cos x) cos x)2 cos x)2 cos x)2 cos x)(z 2 cos x 1 0 1 sin x cos x x 1 1 4t e x 499 1000 4t x 4t x e e 499 499 4t 4t 1000e e 499 499 1000e 4t x 499 e 4t 1000 or x 1 499e 4t 1000 1 499e 4t sin x sin 2 x 1 (1 cos 2 x cos x)(1 1 cos x) cos x) 1 0 z2 0 z 2cos x or cos x (z 2 1 1 1) cos x z2 z2 cos x cos x 2 (b) 500 1 e t 4t 499e 4t 1 does not make sense in this case. z2 z2 1 499 1 1 ln 4 499 (c) From part (b), cos x 1.553 sin 2 x 1 1 Half the population will have heard the rumor in about 1.553 days. dx 1 (c) x(1000 x) dt 250 dx will be greatest when y dt 1 1 cos 2 x (1 (1 z 2)2 z 2)2 x(1000 x) is greatest. (1 1 z 2)2 (1 z 2)2 (1 z 2)2 2z 2 4z 2 z 2 )2 2z 1 z2 z 4 1 2z 2 (1 z 2)2 z4 This occurs when x t dy 48. dx 500 which occurs when 1.553 as shown in part (b). 2x 1 x2 2x 2 dx 1 x2 (1 ds 1 sin x Only sin x x 2 2z 1 z2 x4 2x2 1 (1 x 2)2 x2 1 dx 1 x2 x2 x2 1 dx for 0 1 1/2 0 makes sense in this case. (d) z x 1 2 tan dz dz dz dx 1 x sec 2 dx 2 2 1 1 2 1 (1 2 1 2 dz z2 Arc length x2 1 x2 x2 x2 x2 2 x2 1/2 0 x2 x2 1 dx 1 tan 2 x dx 2 1 1 1 2 1 A 2 x2 1 B x 1 z 2) dx 1 1 1 2 x 1 where A x x2 1 and B 1 dx 1 0 1 1/2 1 x 1 2 1 x 1 x 1 1 dx 1/2 ln x ln 1 2 1 2 1 ln 3 2 ln x 1 0 ln 3 ...
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