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Fundamentals of Differential Equations and Boundary Value Problems
- What term(s) should appear in the partial fraction decomposition of a proper rational function with each of the following? a. A factor of x-3 in the denominator b. A factor of (x-4)³ in the denominator c. A factor of x² + 2x+6 in the denominator a. When a proper rational function has factor of x-3 in the denominator, which of the following should appear in its partial fraction decomposition? Choose the correct answer below. Ax x-3 OA. B. C. ) D. A x-3 Ax A x-3' x-3 A₁ A₂ x-3' x-3arrow_forwardSeparate the following fraction using partial fractions. DO NOT SOLVE for the constants A, B, C, etc. 3x² +4x5 x(x+1)² (x²+1) (x² -4) f(x) = = ...arrow_forward3. a. Express in partial fractions 4х +5 (1–x*)(x+1)* - X 10–11x b. Express in partial fractions (x– 4)(x² + 1)arrow_forward
- S= 3x5 3x4+6x³3x² - 6x + In Evaluate O x² - 4x 2 O x² - 4x 2 x²-2x-In O x2−2x 2 + In + In -dx using method of partial fractions. +C +C (x-1) 1/6(x+2) 16/3 (x+1) 1/2 (x-1) 1/6(x+2) 16 16/3 x + 1 (x-1) 1/6(x+2) 16/3 (x+1) 1/2 (x-1) 1/6(x+2) 16/3 (x+1) 1/2 +C Carrow_forward4. Given a rational function: r(x) = 3x2-2x+4 x3-2x–4x+8 Factor the denominator completely. Make sure you justify your answer by showing all the steps. a. Use part (a) to write the form of the partial fraction decomposition for r(x). Make sure you justify your answer by showing all the steps. b. Page 1 of 2 Simplify part (b) to set up a system of linear equations to find the coefficients of the partial fraction decomposition. Make sure you justify your answer by showing all the steps. C.arrow_forward4. Use the method of partial fractions to evaluate 5x² - 3x + 2 -dx. x³ 2x²arrow_forward
- 1. The form of the partial fractions expansion of the rational function (x²+9z+45) (x-4)², where A, B, C, D are contants, is: OA. OB. O C. Ax+B Cr+D + (x²-4) x²+9x+45 B Cx+D (x-4)² x²+9x+45 B Cx+D + (x+2) x²+9x+45 + + + Ca+D + x²+9x+45 x-4 A (x-2) Ax+B (x-4)² OE. None of thesearrow_forwardQUESTION 9 S x²-2x-In + In Evaluate 3x5 3x4+6x³-3x² - 6x O x2−2x 2 O x² - 4x O x² - 4x 2 て + In + In -dx using method of partial fractions. +C (x − 1) 1/6(x+2) 16/ (x+1) 1/2 (x-1) 1/6(x+2) 16/3- (x+1) 1/2 (x − 1) 1/6(x+2) 16/3- x + 1 (x-1) 1/6(x+2) 16/3 (x+1) 1/2 +C +C ²] + c Carrow_forward
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