Write TRUE if the statement is correct, otherwise, write FALSE. If your answer is false, provide a counterexample, a short explanation, OR modify the statement to make it true. 1. If f is continuous on [a, b), then f is differentiable on (a, b). 2. If f and g are differentiable at a point a E R, then lim fS(2) ± g(x)] exist. 3. If f(a) does not exist for a e R, then the f is not differentiable at z=a.
Write TRUE if the statement is correct, otherwise, write FALSE. If your answer is false, provide a counterexample, a short explanation, OR modify the statement to make it true. 1. If f is continuous on [a, b), then f is differentiable on (a, b). 2. If f and g are differentiable at a point a E R, then lim fS(2) ± g(x)] exist. 3. If f(a) does not exist for a e R, then the f is not differentiable at z=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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![Write TRUE if the statement is correct, otherwise, write FALSE. If your answer is false,
provide a counterexample, a short explanation, OR modify the statement to make it true.
1. If f is continuous on [a, b), then f is differentiable on (a, b).
2. If f and g are differentiable at a point a ER, then lim[f(x) + g(x)] exist.
3. If f(a) does not exist for a E R, then the f is not differentiable at r= a.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F817af78d-71d0-45e6-950d-c0be5f28ba46%2F65d5428b-477c-46e6-9e55-bc457b63e020%2F8cqlfj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Write TRUE if the statement is correct, otherwise, write FALSE. If your answer is false,
provide a counterexample, a short explanation, OR modify the statement to make it true.
1. If f is continuous on [a, b), then f is differentiable on (a, b).
2. If f and g are differentiable at a point a ER, then lim[f(x) + g(x)] exist.
3. If f(a) does not exist for a E R, then the f is not differentiable at r= a.
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