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1. Which of the following are proper rational functions? 4 x? +12 (a) (c) 3 9...
32 , 42 332 CHAPTER 4 Polynomial Functions and Rational Functions 56.7x2 + 4x In Exercises 5 g(x) 57. What are 58. What is th 59. Given an inputs. 60. Movie Tic movie tic years, risi (Source: ers). Usin function, Let xrерr Then use price of a Using synthetic division, determine whether the numbers are zeros of the polynomial function. 31. -3,2; f(x) = 3x + 5x2 - 6x + 18 (32. -4,2; f(x) = 3x + 11x? - 2x...
Question 5 Write the partial fraction decomposition of the rational function -16 x(x-4) 3 X x-4 3 X X-4 4 -+ X 3 x+4 4 X x+4 4 3 X x-4 寸| Question 5 Write the partial fraction decomposition of the rational function -16 x(x-4) 3 X x-4 3 X X-4 4 -+ X 3 x+4 4 X x+4 4 3 X x-4 寸|
What form of the partial fraction decomposition is correct for the following rational function? x² – 3x +7 (x2 - 4x + 6)2(x4 – 1)(x + 1) Select one: O a. . A B C x+1 . x - 1(x + 1)2 - + - Dx + E x2 - 4x + 6 + - F + G (x2 - 4x + 62 + Hx + I x2 - 1 O b. B A B C Dx + Fx +...
(1 point) Evaluate the integral. Loretiste 23+2 dz (1 + 7)(3+5) Answer: (1 point) The form of the partial fraction decomposition of a rational function is given below. (3,2 + 4.1 +43) (1 + 4)(72 +9) А T +4 Br +C 1? +9 A= 3 B= 0 C= 4 Now evaluate the indefinite integral. si (3:2 + 4x + 43) dr = 3/(x+4)+4/(x^2+9) (1 + 4)(x2 +9)
(2) Calculate the following integrals: х 2.x3 – 4x + 3 -dx (x + 1)2(x2 +1) Java 2 - 25 2 dx x4V x2 – 25 (3) Explain why, using the techniques we've learned so far, we are able to calculate the integral of any rational function. (A rational function is one of the form p(x) where g(x2) p and q are polynomials.)
208 and 212 please ❤️ Evaluate the following integrals, which have irreducible quadratic factors. 207. 2 -dx (x – 4) (x2 + 2x + 6) s . x2 208. -dx x3 – x2 + 4x - 4 209. x3 + 6x2 + 3x + 6 -dx x3 + 2x2 _ - 210. -dx (x - 1)(x2 + 2x + 2) Use the method of partial fractions to evaluate the following integrals. 3x + 4 211. -dx (x2 + 4) (3...
(5.6.21 from Stewart and Day) If a factor of the denominator of a rational function is an irreducible quadratic, such as x2+1, the corresponding partial fraction has a linear numerator. For instance, Bx+c f(x) = 2x2+x+1 Determine the values of A, B, and C and use them to evaluate x2+1 x(x2+1) f(x)dx. Use C as your constant of integration, and don't forget to use absolute value bars where needed. | axlox f(x) dx = (5.6.20 from Stewart and Day) If...
3) Sketch the graph of the following rational functions. 2 a. f(x) = + +5r+6 x + 1 b. f(x) - 4x - 32 4) Solve each inequality. Give each solution in interval notation. a. + +8r+15 so b. 2x-5x > 3 C. (x - 1)(x+3)(x+5) > 0 x+3 d. > 0 x² - 5x+6 X +3 <2 2x+4 e.
5) Find the Partial Decomposition of each rational expression. 5x-2 b) (a2-4)(x+1) b) 23+2x2+x
Which of the following is / are true? A. x^-2-x^-1/x-1 is a rational expression. B.(9+X/9-x^2-1/3-x)(X+3/3)=(3/3-x) C. x^2+5x+6/2x^2-x-3÷2x^2+10x+12/(3-2x)(X+1)=1/2 1. Only A 2. Only B 3. Only C 4. Only B and C 5. None of them