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Limits and continuity Which of the following statements are true, and which are false? If true, say why; if false, give a counter- example (that is, an example confirming the falsehood). a. If lim, e f(x) exists but lim, e g(x) does not exist, then lim, f(x) + g(x) does not exist. b. If neither lim, e f(x) nor lim, e g(x) exists, then lim, e (fx) + g(x)) does not exist. c. If f is continuous at x, then so is |f|. d. If |f| is continuous at c, then so is f.

Limits and continuity Which of the following statements are true, and which are false? If true, say why; if false, give a counter- example (that is, an example confirming the falsehood). a. If lim, e f(x) exists but lim, e g(x) does not exist, then lim, f(x) + g(x) does not exist. b. If neither lim, e f(x) nor lim, e g(x) exists, then lim, e (fx) + g(x)) does not exist. c. If f is continuous at x, then so is |f|. d. If |f| is continuous at c, then so is f.

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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Limits and continuity Which of the following statements are true, and which are false? If true, say why; if false, give a counterexample (that is, an example confirming the falsehood).

Limits and continuity Which of the following statements are true, and which are false? If true, say why; if false, give a counter- example (that is, an example confirming the falsehood). a. If lim, e f(x) exists but lim, e g(x) does not exist, then lim, f(x) + g(x) does not exist. b. If neither lim, e f(x) nor lim, e g(x) exists, then lim, e (fx) + g(x)) does not exist. c. If f is continuous at x, then so is |f|. d. If |f| is continuous at c, then so is f.
Transcribed Image Text:Limits and continuity Which of the following statements are true, and which are false? If true, say why; if false, give a counter- example (that is, an example confirming the falsehood). a. If lim, e f(x) exists but lim, e g(x) does not exist, then lim, f(x) + g(x) does not exist. b. If neither lim, e f(x) nor lim, e g(x) exists, then lim, e (fx) + g(x)) does not exist. c. If f is continuous at x, then so is |f|. d. If |f| is continuous at c, then so is f.
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