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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.1: Limits

Problem 14E

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