Suppose that Q(x) (x a)(x b), where a b, and let P Q be a proper rational function so that (a) Show that (b) Use this result to find the partial fraction decomposition for P(x) 3x 2 and Q(x) x 2 4x 12 P(x) Q(x) A (x a) B (x b)...

a Clearing denominators gives us Setting x a then yields while setting x b yields therefore ...

Suppose that Q(x) = (x a)(x b), where a b, and let P/Q be

Question:

Suppose that Q(x) = (x − a)(x − b), where a ≠ b, and let P/Q be a proper rational function so that

P(x) Q(x) A (x-a) + B (x-b)

(a) Show that A = P(a) Q'(a) and B= P(b) Q' (b)

(b) Use this result to find the partial fraction decomposition for P(x) = 3x − 2 and Q(x) = x²− 4x − 12.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 02, 2023 11:05 PM

See More Questions

A first step to checking the ADA accessibility of your site may be to: Remove all small type from the site Purchase a site that claims to be ADA compliant Ask your website provider about current...
The process of adding rational functions (ratios of polynomials) by placing them over a common denominator is the analogue of adding rational numbers. The reverse process of taking a rational...
The process of adding rational functions (ratios of polynomials) by placing them over a common denominator is the analogue of adding rational numbers. The reverse process of taking a rational...
The following table includes the GNP(X) and the demand for food (Y) for a country over ten years period. Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 Y 6 7 8 10 8 9 10 9 11 10 X 455555 50...
Candice Hargrove, the accountant, is a perfectionist. No one can do the job as well as she can. Indeed, she has found budget information provided by the various departments to be worthless. She must...
A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping...
Thermal regeneration of a fixed-bed adsorber is based on the fact that the adsorption process is exothermic; therefore, heating the saturated adsorbent will result in desorption. The dynamics of the...
Klandon Company manufactures decorative rocks for aquariums. Kim Klandon is preparing the budget for the quarter ended June 30. She has gathered the following information. 1. Klandons sales manager...
Translate the following business rules into an object relational diagram (ORD) using UMLet (See the above Object Relational Diagram examples). a USER has many ROLES. a USER has one BIRTHDATE. a USER...
Prove the general formula where a, b are constants such that a b. dx (x-a)(x - b) S 1 In a-b x-al + C x-b|
Use the substitution of Exercise 57 to evaluate d/cos + sin . Data From Exercise 57 Show that the substitution = 2 tan 1 t (Figure 2) yields the formulas This substitution transforms the integral...
For Exercises classify each as nominal-level, ordinal-level, interval level, or ratio-level measurement. Amounts of money spent on a medical checkup
You have been appointed to manage a large R&D laboratory. You find a high level of conflict between scientists in the unit. Why might this conflict be arising? How will you try to resolve it?
How does r-strategy differ from K-strategy? How does a specialist strategy differ from a generalist strategy? Use companies in the fast-food industry to provide an example of each strategy.
How can the design of the organizations structure and culture give some subunits more power than others?
Your grandfather would like to share some of his fortune with you. He offers to give you money under one of the following scenarios (you get to choose): 1. $8,550 per year at the end of each of the...
Refer to the information about Dabaneh Corporation in Exercise E26-19. Assume the project has no residual value. Compute the ARR for the equipment. Data From Exercise E26-19: Dabbaneh Corporation is...
Cameron Manufacturing produces auto parts for auto manufacturers and parts wholesalers. The business is very competitive, and productivity measures are used throughout its eight manufacturing plants....
If 2 5 9 - k 5 8 = 2 5 8 , what is the value of k?
True or False Every polynomial function of degree 3 with real coefficients has exactly three real zeros.
If r is a real zero of even multiplicity of a function f, then the graph of f _______ (crosses/touches) the x-axis at r.
In problem, use the graph of the function f to solve the inequality. (a) f(x) > 0 (b) f(x) ¤ 0 3 y = 1 3 4 5 x -4 -3 -2 -2 x= 2 X=-1
Part 1 The question at hand: On average, how many Skittles are in a 2.17 oz. bag? Wrigley's, the maker of Skittles, claims that there is an average of 56 pieces in each 2.17 oz. bag. We will conduct...
Players A and B each pick a number between 1 and 100. The game is a draw if both players pick the same number. Otherwise, the player who picks the smaller number wins unless that smaller number is...
You are interested in learning who makes the best burrito close to campus in Eugene. So, you go Burrito Boy, El Super Burrito, Burritos Amigo, and Chipotle and ask patrons who ordered a chicken-...

Suppose that Q(x) = (x a)(x b), where a b, and let P/Q be

Question:

P(x) Q(x) A (x-a) + B (x-b)

Step by Step Answer:

a Clearing denominators gives us Setting x a then yields while setting x b yields therefore ...View the full answer

Calculus

Students also viewed these Mathematics questions