Download Partial Fractions - Calculus - Exercise and more Exercises Calculus in PDF only on Docsity! Partial Fractions Find the partial fraction decomposition. 1) 3 x2 + 4x + 3 = A x + 3 + B x + 1 A) A = 3 2 , B = - 3 2 B) A = - 3 2 , B = - 3 2 C) A = - 3 2 , B = 3 2 D) A = 3 2 , B = 3 2 2) -7 x(3x - 1)(x + 1) = A x + B 3x - 1 + C x + 1 A) A = -7, B = 63 4 , C = 7 4 B) A = 7, B = - 63 4 , C = - 7 4 C) A = 7, B = 63 4 , C = 7 4 D) A = -7, B = - 63 4 , C = - 7 4 3) 5x - 2 x3 - 4x = A x + B x + 2 + C x - 2 A) A = - 1 2 , B = 1, C = 3 2 B) A = 1 2 , B = 1, C = - 3 2 C) A = - 1 2 , B = 3 2 , C = 1 D) A = 1 2 , B = - 3 2 , C = 1 4) x - 1 (x + 2)(x - 3)2 = A x + 2 + B x - 3 + C (x - 3)2 A) A = 3 25 , B = - 3 25 , C = 2 5 B) A = - 3 25 , B = - 3 25 , C = 2 5 C) A = - 3 25 , B = 3 25 , C = 2 5 D) A = 3 25 , B = 3 25 , C = 2 5 5) x + 2 (x - 1)2(x + 5) = A x - 1 + B (x - 1)2 + C x + 5 A) A = - 1 12 , B = 1 2 , C = - 1 12 B) A = 1 12 , B = - 1 2 , C = - 1 12 C) A = - 1 12 , B = 1 2 , C = 1 12 D) A = 1 12 , B = 1 2 , C = - 1 12 6) x - 1 x3 - x2 - 4x = A x + Bx + C x2 - x - 4 A) A = 1 4 , B = - 1 4 , C = 5 4 B) A = - 1 4 , B = - 1 4 , C = 5 4 C) A = 1 4 , B = 1 4 , C = - 5 4 D) A = - 1 4 , B = 1 4 , C = 5 4 PreCalculus 7) x + 3 x3 + 64 = A x + 4 + Bx + C x2 - 4x + 16 A) A = 1 48 , B = 1 48 , C = - 5 6 B) A = 1 48 , B = - 1 48 , C = 5 6 C) A = - 1 48 , B = - 1 48 , C = 5 6 D) A = - 1 48 , B = 1 48 , C = 5 6 8) 5 x(x2 + 3) = A x + Bx + C x2 + 3 A) A = 5 6 , B = - 5 6 , C = 0 B) A = - 5 6 , B = 5 6 , C = 0 C) A = 5 3 , B = - 5 3 , C = 0 D) A = - 5 3 , B = 5 3 , C = 0 9) 2x + 1 (x + 1)(x2 + 2) = A x + 1 + Bx + C x2 + 2 A) A = 5 3 , B = - 1 3 , C = 1 3 B) A = 1 3 , B = - 1 3 , C = 5 3 C) A = 5 3 , B = 1 3 , C = - 1 3 D) A = - 1 3 , B = 1 3 , C = 5 3 10) 4x - 27 (x + 2)(x - 5) A) 5 x + 2 + 1 x - 5 B) 1 x - 5 - 5 x + 2 C) 5 x + 2 - 1 x - 5 D) 4 x + 2 - 27 x - 5 11) - 31x - 131 2x2 + 23x + 56 A) - 5 2x - 7 - 13 x - 8 B) - 5 2x + 7 - 13 x + 8 C) 5 2x + 7 + 13 x + 8 D) - 5 x + 7 - 13 2x + 8 12) 31x - 80 6x2 - 31x + 40 A) 5 2x - 5 - 8 3x - 8 B) 5 2x + 5 + 8 3x + 8 C) 8 3x - 8 - 5 2x - 5 D) 5 2x - 5 + 8 3x - 8 13) 5 9x2 - 25 A) 1/2 3x - 5 + -1/2 3x + 5 B) 1/2 3x - 5 + -1/2 (3x - 5)2 C) 1 3x - 5 + -1 3x + 5 D) 1/2 3x + 5 + -1/2 3x - 5 Calin M. Agut - 2012