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- Determine the behavior off(x) = (x-1)(x+2)' x → 1- f (x) →_ x → 1+ f(x) →. x → -2- f(x) → x → -2+ f(x) →. х — — о f (x) →_ X → ∞ f (x) →,

- Determine the behavior off(x) = (x-1)(x+2)' x → 1- f (x) →_ x → 1+ f(x) →. x → -2- f(x) → x → -2+ f(x) →. х — — о f (x) →_ X → ∞ f (x) →,

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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**Problem:** Determine the behavior of \( f(x) = \frac{x}{(x-1)(x+2)} \). 1. \( x \to 1^- \) \( f(x) \to \) ____________ 2. \( x \to 1^+ \) \( f(x) \to \) ____________ 3. \( x \to -2^- \) \( f(x) \to \) ____________ 4. \( x \to -2^+ \) \( f(x) \to \) ____________ 5. \( x \to -\infty \) \( f(x) \to \) ____________ 6. \( x \to \infty \) \( f(x) \to \) ____________ **Explanation:** The function given is \( f(x) = \frac{x}{(x-1)(x+2)} \), which is a rational function. To determine the behavior of \( f(x) \), we evaluate the limits as \( x \) approaches critical points and infinity. These points include the vertical asymptotes at \( x = 1 \) and \( x = -2 \), and the behavior as \( x \to -\infty \) and \( x \to \infty \).
Transcribed Image Text:**Problem:** Determine the behavior of \( f(x) = \frac{x}{(x-1)(x+2)} \). 1. \( x \to 1^- \) \( f(x) \to \) ____________ 2. \( x \to 1^+ \) \( f(x) \to \) ____________ 3. \( x \to -2^- \) \( f(x) \to \) ____________ 4. \( x \to -2^+ \) \( f(x) \to \) ____________ 5. \( x \to -\infty \) \( f(x) \to \) ____________ 6. \( x \to \infty \) \( f(x) \to \) ____________ **Explanation:** The function given is \( f(x) = \frac{x}{(x-1)(x+2)} \), which is a rational function. To determine the behavior of \( f(x) \), we evaluate the limits as \( x \) approaches critical points and infinity. These points include the vertical asymptotes at \( x = 1 \) and \( x = -2 \), and the behavior as \( x \to -\infty \) and \( x \to \infty \).
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