3. Let a € R. Let f and g be two different functions defined on R. Is each of the following claims true or false? Prove your answer. If it is true, prove it directly from the epsilon-delta definition of a limit. Hint: often times, the easiest way to prove something is false is by providing a counter example and and proving that counter example satisfies the required conditions. (a) IF f(x) is not continuous at a and g(x) is not continuous at a, THEN f(x)g(x) is not continuous at a. False True (b) IF f(x) is not continuous at a and g(x) is not continuous at a, THEN f(x)/g(r) is not continuous at a. True False
3. Let a € R. Let f and g be two different functions defined on R. Is each of the following claims true or false? Prove your answer. If it is true, prove it directly from the epsilon-delta definition of a limit. Hint: often times, the easiest way to prove something is false is by providing a counter example and and proving that counter example satisfies the required conditions. (a) IF f(x) is not continuous at a and g(x) is not continuous at a, THEN f(x)g(x) is not continuous at a. False True (b) IF f(x) is not continuous at a and g(x) is not continuous at a, THEN f(x)/g(r) is not continuous at a. True False
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Let a € R. Let f and g be two different functions defined on R. Is each of the following claims true
or false? Prove your answer. If it is true, prove it directly from the epsilon-delta definition of a limit.
Hint: often times, the easiest way to prove something is false is by providing a counter example and
and proving that counter example satisfies the required conditions.
(a) IF f(x) is not continuous at a and g(x) is not continuous at a,
THEN f(x)g(x) is not continuous at a.
False
True
(b) IF f(x) is not continuous at a and g(x) is not continuous at a,
THEN f(x)/g(x) is not continuous at a.
True False
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