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Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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**Finding Limits: An Introduction**

This exercise is designed to help you understand the concept of limits in calculus. For each function below, determine the limit as \(x\) approaches a specified value. If a limit does not exist, provide a rationale for why it does not.

1. **Limit Problem 1:**
   \[
   \lim_{{x \to 1}} \frac{{x^2 + 2x - 3}}{{x - 1}}
   \]

2. **Limit Problem 2:**
   \[
   \lim_{{x \to 8}} \frac{{x^2 - 16}}{{x^2 + x - 72}}
   \]

3. **Limit Problem 3:**
   \[
   \lim_{{x \to -9}} \frac{{5}}{{x}}
   \]

**Instruction:**
Analyze each limit problem. Simplify the expressions where possible or use other limit laws and techniques to find the limit. If the limit does not exist, provide detailed reasoning, considering aspects like asymptotic behavior or discontinuity.
Transcribed Image Text:**Finding Limits: An Introduction** This exercise is designed to help you understand the concept of limits in calculus. For each function below, determine the limit as \(x\) approaches a specified value. If a limit does not exist, provide a rationale for why it does not. 1. **Limit Problem 1:** \[ \lim_{{x \to 1}} \frac{{x^2 + 2x - 3}}{{x - 1}} \] 2. **Limit Problem 2:** \[ \lim_{{x \to 8}} \frac{{x^2 - 16}}{{x^2 + x - 72}} \] 3. **Limit Problem 3:** \[ \lim_{{x \to -9}} \frac{{5}}{{x}} \] **Instruction:** Analyze each limit problem. Simplify the expressions where possible or use other limit laws and techniques to find the limit. If the limit does not exist, provide detailed reasoning, considering aspects like asymptotic behavior or discontinuity.
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