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Using Partial Fractions In Exercises 3-20, use partial fractions to find the indefinite
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CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
- partial fraction decomposition to find 3x²+x-8 x(x - 2)² dxarrow_forwardA right triangle has one vertex on the graph of y =x°, x> 0, at (x, y), another at the origin, and the third on the positive y-axis at (0, y), as shown in the figure. Express the area A of the triangle as a function of x. y = x (0, у) (x, y) A(x) = %3D (Use integers or fractions for any numbers in the expression.) -> (0, 0)arrow_forwardQuestions Use Partial Fraction method to evaluate * xp 4x² – 4x + 1 - 1 Add file Evaluate the integralarrow_forward
- Partial Fraction: Evaluate integralarrow_forwardA right triangle has one vertex on the graph of y = x, x>0, at (x, y), another at the origin, and the third on the positive y-axis at (0, y), as shown in the figure. Express the area A of the triangle as a function of x. y=x5 (0. y) (x, y) A(x) =D (Use integers or fractions for any numbers in the expression.) (0, 0)arrow_forwardUse partial fractions to find the integral. 4- X | 2x² 2x² + x1 Step 1 Rewrite the polynomial as 2x² + x1 = 2x² - x + 2x - 1. Collect the terms according to the power of x on the right side and factorize. 2x² + 2x -x-1 = x(2x − 1) + (2x - 1) = (2x - 1)(x + 1) Because 2x² + x − 1 = (2x − 1)(x + 1), you should include one partial fraction for each factor and write A 4-X 2x²+x-1 where A and B are to be determined. dx To solve for A, let x = 1/2✔ 1 x 2 4 2x Step 2 Multiplying this equation by the least common denominator (2x - 1)(x + 1) yields the basic equation 4x = A(x+1 + B(2x - 1). Step 3 The most convenient values are the ones that make particular factors equal to 0. 7 x+1 Because this equation is to be true for all x, substitute any convenient values for x to obtain equations in A and B. Step 4 To solve for B, let x = 4 1/2 and obtain 4 − —⁄2 = A ( ²¹1 + 1) + B( ² × 1⁄2 − 1) 2 - 2 A = 7/3 X = AX 4 + 1 = A(-1 2x = 4 B = -5/3 1 2 + 5 x 7/3 x X to obtain the following. + 1) + B(2(-1 B X…arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage