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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 2e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 2e

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# Give an example of each of the following.a. A simple

ISBN: 9780321570567 2

## Solution for problem 2E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Problem 2E

Give an example of each of the following.a. A simple linear factor________________b. A repeated linear factor________________c. A simple irreducible quadratic factor________________d. A repealed irreducible quadratic factor

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Problem 2ESolution:-Step1a. A simple linear factordefinition: linear factor 1) words: “linear factor with root r ” 2) usage: r is a some real number 3) meaning: the expression ( x r) Example The polynomial f(x)= can be written as a product of linear factors, f(x)=(x+1)(x-1)(x-2) . Step2b. A repeated linear factorExample 2x+2=Ax-A+bAt A=2-A+B=2-2+B=2B=2+2=4 Step3c. A simple irreducible quadratic factorExample I =First, complete the square: + 4x + 7 = + 3. Thus I = In the first of these two integrals, the numerator x is not a constant multiple of the derivative 2(x + 2) of the denominator, so substitution does not work. Substitute for the quantity in the completion of the square: let y = x+ 2, so x = y 2 and dx = dy. Hence I = Now split it up. I is the sum of =And The final answer, expressed in terms of x is ++ C. Step4d. A repeated irreducible quadratic factorExamplef (x) = Comparing numerators, we have5x2+20x+6 = A(x+1)2+Bx(x+1)+Cx.Taking x = 0, we find A = 6. Likewise, taking x = -1, we find that C = 9. To determine B, substitute any convenient value for x, say x = 1. (Unfortunately, notice that there is no choice of x that will make the two terms containing Aand C both zero, without also making the term containing B zero.) You should find that B = -1. So, we have = 6ln | x| -ln | x+1| -9(x+1)-1+c.

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##### ISBN: 9780321570567

This full solution covers the following key subjects: factor, quadratic, simple, irreducible, Linear. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 2E from chapter: 7.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 2E from 7.4 chapter was answered, more than 400 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Give an example of each of the following.a. A simple linear factor________________b. A repeated linear factor________________c. A simple irreducible quadratic factor________________d. A repealed irreducible quadratic factor” is broken down into a number of easy to follow steps, and 26 words.

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