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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![### Evaluating Limits in Calculus
In this exercise, you'll evaluate the following limit expression:
\[ \lim_{{x \to -8}} \left( \frac{{-2x^2 - 20x - 32}}{{x + 8}} \right) \]
To solve this limit, follow these steps:
1. **Factor the numerator**: Identify common factors or use factoring techniques such as grouping or factoring quadratic equations.
2. **Simplify the expression**: Cancel out common factors in the numerator and the denominator, if possible.
3. **Substitute the limit**: After simplification, substitute \( x = -8 \) into the remaining expression to evaluate the limit.
This problem emphasizes important concepts in calculus, such as factoring and simplifying rational expressions as well as substituting values into limits. Solving these types of problems helps build foundational skills necessary for more advanced topics in calculus.
Your solution should be entered in the box provided below the limit expression. Good luck!
Box: [Text box for answer input]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F492efe9f-0a9a-45cd-99ee-2fd493a23754%2F42a9c48f-6b58-47fd-afb9-d5aa96dc6c11%2Fbjbqkk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Limits in Calculus
In this exercise, you'll evaluate the following limit expression:
\[ \lim_{{x \to -8}} \left( \frac{{-2x^2 - 20x - 32}}{{x + 8}} \right) \]
To solve this limit, follow these steps:
1. **Factor the numerator**: Identify common factors or use factoring techniques such as grouping or factoring quadratic equations.
2. **Simplify the expression**: Cancel out common factors in the numerator and the denominator, if possible.
3. **Substitute the limit**: After simplification, substitute \( x = -8 \) into the remaining expression to evaluate the limit.
This problem emphasizes important concepts in calculus, such as factoring and simplifying rational expressions as well as substituting values into limits. Solving these types of problems helps build foundational skills necessary for more advanced topics in calculus.
Your solution should be entered in the box provided below the limit expression. Good luck!
Box: [Text box for answer input]
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