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Prove that if f(x) and g(x) are continuous at a and c is a constant, then the function cf(x) + g(x) is also continuous at a. Hint: You need to use Limit Laws - this is similar to the proof of Theorem 4.

Prove that if f(x) and g(x) are continuous at a and c is a constant, then the function cf(x) + g(x) is also continuous at a. Hint: You need to use Limit Laws - this is similar to the proof of Theorem 4.

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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The book is called ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS second edition

1. Read Theorem 4 (on pg. 49 of the virtual textbook) about the sum, difference, constant multiple, product, and quotient of continuous functions at a point. Prove that if f(x) and g(x) are continuous at a and c is a constant, then the function cf(x) + g(x) is also continuous at a. Hint: You need to use Limit Laws - this is similar to the proof of Theorem 4.
Transcribed Image Text:1. Read Theorem 4 (on pg. 49 of the virtual textbook) about the sum, difference, constant multiple, product, and quotient of continuous functions at a point. Prove that if f(x) and g(x) are continuous at a and c is a constant, then the function cf(x) + g(x) is also continuous at a. Hint: You need to use Limit Laws - this is similar to the proof of Theorem 4.
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