x² - 25 lim x→-5 x+5

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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The image contains a mathematical limit expression. Here is the transcription suitable for an educational website:

---

**Mathematical Limit:**

\[
\lim_{{x \to -5}} \frac{{x^2 - 25}}{{x + 5}}
\]

**Explanation:**

This limit expression requires evaluating the limit as \( x \) approaches -5 for the function \( \frac{{x^2 - 25}}{{x + 5}} \). To simplify this function, recognize that \( x^2 - 25 \) can be factored into \( (x - 5)(x + 5) \).

Substituting back into the limit expression, we get:

\[
\lim_{{x \to -5}} \frac{{(x - 5)(x + 5)}}{{x + 5}}
\]

We can cancel the common factor of \( x + 5 \) in the numerator and the denominator:

\[
\lim_{{x \to -5}} (x - 5)
\]

Now, substituting \( x = -5 \):

\[
-5 - 5 = -10
\]

Hence, the limit is:

\[
-10
\]

Understanding this process helps in comprehending the behavior of functions involving polynomials and their limits.

---
Transcribed Image Text:The image contains a mathematical limit expression. Here is the transcription suitable for an educational website: --- **Mathematical Limit:** \[ \lim_{{x \to -5}} \frac{{x^2 - 25}}{{x + 5}} \] **Explanation:** This limit expression requires evaluating the limit as \( x \) approaches -5 for the function \( \frac{{x^2 - 25}}{{x + 5}} \). To simplify this function, recognize that \( x^2 - 25 \) can be factored into \( (x - 5)(x + 5) \). Substituting back into the limit expression, we get: \[ \lim_{{x \to -5}} \frac{{(x - 5)(x + 5)}}{{x + 5}} \] We can cancel the common factor of \( x + 5 \) in the numerator and the denominator: \[ \lim_{{x \to -5}} (x - 5) \] Now, substituting \( x = -5 \): \[ -5 - 5 = -10 \] Hence, the limit is: \[ -10 \] Understanding this process helps in comprehending the behavior of functions involving polynomials and their limits. ---
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