Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![**Partial Fraction Decomposition**
The task is to find the partial fraction decomposition for the function given below:
\[
\frac{2}{{x^2 - 2x - 8}}
\]
This function needs to be expressed in terms of simpler fractions that can be more easily integrated or manipulated.
**Decomposition Formula**
To find the decomposition, assume:
\[
\frac{2}{{x^2 - 2x - 8}} = \text{(To be completed)}
\]
Fill in the box with the appropriate partial fraction form. For quadratics that can be factored into linear terms, use:
\[
\frac{A}{{x - r_1}} + \frac{B}{{x - r_2}}
\]
where \(r_1\) and \(r_2\) are the roots of the quadratic \(x^2 - 2x - 8\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1913c9c-da59-4e5e-af1e-78b6351c7d9b%2F60446c9f-cdfb-4a24-9ccb-c76aaab99328%2Fuxycwkr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Partial Fraction Decomposition**
The task is to find the partial fraction decomposition for the function given below:
\[
\frac{2}{{x^2 - 2x - 8}}
\]
This function needs to be expressed in terms of simpler fractions that can be more easily integrated or manipulated.
**Decomposition Formula**
To find the decomposition, assume:
\[
\frac{2}{{x^2 - 2x - 8}} = \text{(To be completed)}
\]
Fill in the box with the appropriate partial fraction form. For quadratics that can be factored into linear terms, use:
\[
\frac{A}{{x - r_1}} + \frac{B}{{x - r_2}}
\]
where \(r_1\) and \(r_2\) are the roots of the quadratic \(x^2 - 2x - 8\).
Expert Solution
Step 1: Decompose in partial fraction
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