Determine whether each of the following statements is always ta circle hat is, provide an explicit example or sketch where the staten lain why your example is relevant. your answer. If the statement is false, provide a If lim f(x) = o and lim g(x) =0, then lim f(r) g(x)- 2

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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6.
Determine whether each of the following statements is always true or may
be false, and circle your answer. If the statement is false, provide a counter-
example. That is, provide an explicit example or sketch where the statement is not
true, and explain why your example is relevant.
(a)
If lim f(r) = 00 and lim g(r) = 0, then lim f(r) - g(r) = 0.
True
False, counter-example:
(b)
max of f.
If f(x) has a critical point at z = c, then f(c) is a local min or a local
True
False, counter-example:
Transcribed Image Text:6. Determine whether each of the following statements is always true or may be false, and circle your answer. If the statement is false, provide a counter- example. That is, provide an explicit example or sketch where the statement is not true, and explain why your example is relevant. (a) If lim f(r) = 00 and lim g(r) = 0, then lim f(r) - g(r) = 0. True False, counter-example: (b) max of f. If f(x) has a critical point at z = c, then f(c) is a local min or a local True False, counter-example:
エ
(c)
lim
1+
= e.
True
False, reason:
(d) If f(z) is a differentiable function, it is not possible to have f' and f"
have a sign transition from ++ to +-.
True
False, counter-example:
Transcribed Image Text:エ (c) lim 1+ = e. True False, reason: (d) If f(z) is a differentiable function, it is not possible to have f' and f" have a sign transition from ++ to +-. True False, counter-example:
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