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x² + 2x lim x 1 x² - 2x + 1

x² + 2x lim x 1 x² - 2x + 1

Calculus: Early Transcendentals
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...
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Question
The image shows a mathematical expression representing a limit. The expression is: \[ \lim_{{x \to 1}} \frac{{x^2 + 2x}}{{x^2 - 2x + 1}} \] This represents the limit of the function \(\frac{{x^2 + 2x}}{{x^2 - 2x + 1}}\) as \(x\) approaches 1. The function is a rational expression with a quadratic polynomial in both the numerator (\(x^2 + 2x\)) and the denominator (\(x^2 - 2x + 1\)).
Transcribed Image Text:The image shows a mathematical expression representing a limit. The expression is: \[ \lim_{{x \to 1}} \frac{{x^2 + 2x}}{{x^2 - 2x + 1}} \] This represents the limit of the function \(\frac{{x^2 + 2x}}{{x^2 - 2x + 1}}\) as \(x\) approaches 1. The function is a rational expression with a quadratic polynomial in both the numerator (\(x^2 + 2x\)) and the denominator (\(x^2 - 2x + 1\)).
Expert Solution
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\lim _{x\to 1}\left(\frac{x^2+2x}{x^2-2x+1}\right)

=\lim _{x\to 1}\left(\frac{x\left(x+2\right)}{x^2-x-x+1}\right)

=\lim _{x\to 1}\left(\frac{x\left(x+2\right)}{x\left(x-1\right)-1\left(x-1\right)}\right)

=\lim _{x\to 1}\left(\frac{x\left(x+2\right)}{\left(x-1\right)\left(x-1\right)}\right)

=\lim _{x\to 1}\left(\frac{x\left(x+2\right)}{\left(x-1\right)^2}\right)

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