Mathematic Methods HW Solutions 43

Mathematic Methods HW Solutions 43 - Chapter 8 7.10 7.11...

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Unformatted text preview: Chapter 8 7.10 7.11 7.12 7.13 7.16 7.17 7.18 7.19 7.20 7.21 7.22 7.23 7.25 7.28 8.8 8.10 8.12 8.17 8.22 8.25 8.27 43 √ x = 1 + t2 x = (1 − 3t)1/3 x t = 1 √ 2 (1 − u4 )−1/2 du u t = (ω 2 )−1 (cos θ)−1/2 dθ (a) y = Ax + Bx−3 (b) y = Ax2 + Bx−2 √ √ (c) y = (A + B ln x)/x3 (d) y = Ax cos( 5 ln x) + Bx sin( 5 ln x) y = Ax4 + Bx−4 + x4 ln x y = Ax + Bx−1 + 1 x + x−1 ln x 2 y = x3 (A + B ln x) + x3 (ln x)2 y = x2 (A + B ln x) + x2 (ln x)3 √ √ y = A x sin 23 ln x + γ + x2 y = A cos ln x + B sin ln x + x R = Ar n + Br −n , n = 0; R = A ln r + B , n = 0 R = Ar l + Br −l−1 x−1 − 1 7.26 x2 − 1 7.27 x3 ex 1/3 x 1/x xe 7.29 xe 7.30 (x − 1) ln x − 4x e−2t − te−2t 1t t 3 e sin 3t + 2e cos 3t 3 cosh 5t + 2 sinh 5t 2a(3p2 − a2 )/(p2 + a2 )3 [(p + a)2 − b2 ]/[(p + a)2 + b2 ]2 e−pπ/2 /(p2 + 1) −v (p2 + v 2 )−1 e−px/v = et (3 + 2t) = cos t + 1 (sin t − t cos t) 2 = 1 t3 e3t + 5te3t 6 = t sin 4t = 3t2 e2t = 1 (t2 e−t + 3et −e−t ) 2 = te2t = 1 t sin 3t + 2 cos 3t 6 = 2e−2t −e−t = 2t + 1 = 2 cos t + sin t = (5 − 6t)et − sin t = te−t cos 3t y = t cos t − 1 9.28 z = cos t + t sin t 9.30 y = t − sin 2t z = cos 2t y = sin 2t 9.32 z = cos 2t − 1 8.9 8.11 8.13 8.21 8.23 8.26 et − 3e−2t 4 −2t + 3 et/3 7e 7 −2t e (2 sin 4t − cos 4t) 2b(p + a)/[(p + a)2 + b2 ]2 y = te−2t (cos t − sin t) cos(t − π ), t > π ; 0, t < π = e−2t (4t + 1 t2 ) 2 1 = − 2 t cos t = 1 − e2t = (t + 2) sin 4t = te2t = sinh 2t = 2 sin 3t + 1 t sin 3t 6 =2 = e2t = e3t + 2e−2t sin t = sin t + 2 cos t − 2e−t cos 2t = (3 + t)e−2t sin t 1 = t + (1 − e4t )/4, z = 3 + e4t y = et 9.29 z = t + et 9.31 y = t z = et y = sin t − cos t 9.33 z = sin t 9.2 9.4 9.6 9.8 9.10 9.12 9.14 9.16 9.18 9.20 9.22 9.24 9.26 y y y y y y y y y y y y y 9.3 9.5 9.7 9.9 9.11 9.13 9.15 9.17 9.19 9.21 9.23 9.25 9.27 y y y y y y y y y y y y y 9.34 9.36 9.38 9.40 9.42 3/13 arc tan(2/3) 4/5 1 π/4 9.35 9.37 9.39 9.41 10/262 15/8 ln 2 √ arc tan(1/ 2) ...
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