2. Let a be a real number, and consider the function h: (-∞, a) U (a, ∞) → R defined by h(x) A. The limit lim h(x) intuitively evaluates to +∞. Explain. x→a+ B. The limit lim h(x) intuitively evaluates to -∞o. Explain. x→a¯ C. Based on our results from Parts A and B, the limit lim h(x) does not exist. Explain. = x-a

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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2. Let \( a \) be a real number, and consider the function \( h: (-\infty, a) \cup (a, \infty) \to \mathbb{R} \) defined by \( h(x) = \frac{1}{x-a} \).

A. The limit \( \lim_{x \to a^+} h(x) \) intuitively evaluates to \( +\infty \). Explain.

B. The limit \( \lim_{x \to a^-} h(x) \) intuitively evaluates to \( -\infty \). Explain.

C. Based on our results from Parts A and B, the limit \( \lim_{x \to a} h(x) \) does not exist. Explain.
Transcribed Image Text:2. Let \( a \) be a real number, and consider the function \( h: (-\infty, a) \cup (a, \infty) \to \mathbb{R} \) defined by \( h(x) = \frac{1}{x-a} \). A. The limit \( \lim_{x \to a^+} h(x) \) intuitively evaluates to \( +\infty \). Explain. B. The limit \( \lim_{x \to a^-} h(x) \) intuitively evaluates to \( -\infty \). Explain. C. Based on our results from Parts A and B, the limit \( \lim_{x \to a} h(x) \) does not exist. Explain.
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