Pre-Calc Homework Solutions 361

Pre-Calc Homework Solutions 361 - Chapter 8 Review 8 x 3(x...

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Unformatted text preview: Chapter 8 Review 8 x 3(x 2) x A 2 B x C x2 D x3 361 56. 59. x 3 2) D(x D)x 2) 2D x3 x3 8 Ax 3 (A Bx 2(x B)x 3 2) (2B Cx(x C)x 2 x x3 x3 0x2 0x2 (2C 1 x 1 x+0 x 1 x 1 x(x 2 1) B C x 1 x 1 Equating coefficients of like terms gives A B 0, 2B C 0, 2C D 0, and 2D 8 1 x 1 1 x x3 x A x 1 x x(x 1)(x 1) 1 1 x x(x 1 1)(x 1) Solving the system simultaneously yields A 1, B 8 dx x3(x 2) x 1 A(x (A 1)(x B 1) Bx(x (B 1) C)x A Cx(x 1) 1, C dx x 2 2, D dx x 4 4 dx x3 2 x2 C)x 2 ln x 57. t 3 3t 2 t 3 2 2 dx x2 2 ln x x Equating coefficients of like terms gives A B C 0, B C 1, and A 1. C t 4t t t(t 2 4 Solving the system simultaneously yields 1) A t Bt t2 2 C 1 A (Bt Ct C)t A 60. x 2 x3 x3 1, B 1 dx x 1, C dx x 0 dx x dx x 1 3t 2 4t 4 A(t (A 1) B)t 2 ln x ln x x 0x 3x 3x 1 C Equating coefficients of like terms gives A B 3, C 4 and A 4. 4x 3 x3 x3 4x 2 4x 2 Solving the system simultaneously yields x3 A 3t 2 4, B 4t t3 t 4 1, C dt 4 4 dt t 4 dt t t 4 dt t2 1 t dt 4 dt t2 1 t2 1 1 ln (t 2 1) 4 tan 1 t 2 x 2 (x 4x 2 3x x 4x 3 x 2 4x 3 3x A B 1)(x 3) x 1 x 3 x (x 3x 1)(x 3) 3x 3x C A(x (A 3) B)x B(x 3A 1) B 4 ln t 58. t 4 (t 2 Equating coefficients of like terms gives A B 3, 3A B 0 3 ,B 2 9/2 dx 3 9 . 2 4t 2 1 1)(t 2 3 3) (t 2 At t2 3)(t 2 B 1 1) Ct t2 D 3 Solving the system simultaneously yields A 1) C)t 3B D x3 x 2 1 (At (A B)(t 2 C)t 3 3) (B (Ct D)t 2 D)(t 2 (3A 4x 2 dx 4x 3 x dx x2 2 x 3/2 dx 1 x 3 ln x 2 1 9 ln x 2 3 C Equating coefficients of like terms gives A C 0, B D 0, 3A C 0, and 3B D 1 Solving the system simultaneously yields A (t 2 0, B dt 3)(t 2 1 ,C 2 1) 0, D 1/2 dt t2 1 1 tan 1 t 2 1 2 1/2 dt t2 3 1 1 t tan C 3 2 3 Evaluate the integrals using Formula 16, with x in the first integral and a 3 in the second. t, a 1 ...
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