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 expression represents a mathematical limit:
\[
\lim_{{x \to -6}} \frac{{x + 6}}{{x^2 + 9x + 18}}
\]
Explanation:
This is the limit of a rational function as \( x \) approaches -6. The numerator of the fraction is \( x + 6 \) and the denominator is a quadratic expression \( x^2 + 9x + 18 \). To solve this, one might need to factor the quadratic equation in the denominator and check for any simplifications or cancellations with the numerator. Then, evaluate the limit by substituting \( x \to -6 \) into the simplified expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc657f57-b854-4d07-b552-ddc8fa44d056%2Fe0d3a9e7-5a90-4b0f-bac8-6a5fbef517a9%2Fbe9pqa8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The expression represents a mathematical limit:
\[
\lim_{{x \to -6}} \frac{{x + 6}}{{x^2 + 9x + 18}}
\]
Explanation:
This is the limit of a rational function as \( x \) approaches -6. The numerator of the fraction is \( x + 6 \) and the denominator is a quadratic expression \( x^2 + 9x + 18 \). To solve this, one might need to factor the quadratic equation in the denominator and check for any simplifications or cancellations with the numerator. Then, evaluate the limit by substituting \( x \to -6 \) into the simplified expression.
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