determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, then lim x→7 f(x) = 0. True. If lim x→7 f(x) is not equal to zero and lim x→7 g(x) = 0, then lim x→7 f(x)/g(x) does not exist. True. Any number divided by zero is equal to zero. False. Let g(x) = (x − 7) and f(x) = (x − 1)(x − 7). Then lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 e
determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, then lim x→7 f(x) = 0. True. If lim x→7 f(x) is not equal to zero and lim x→7 g(x) = 0, then lim x→7 f(x)/g(x) does not exist. True. Any number divided by zero is equal to zero. False. Let g(x) = (x − 7) and f(x) = (x − 1)(x − 7). Then lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 e
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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determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If
lim x→7 g(x) = 0
and
lim x→7 f(x)/g(x) = 0
exists, then
lim x→7 f(x) = 0.
True. If lim x→7 f(x) is not equal to zero and lim x→7 g(x) = 0, then lim x→7 f(x)/g(x) does not exist.
True. Any number divided by zero is equal to zero.
False. Let g(x) = (x − 7) and f(x) = (x − 1)(x − 7). Then lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, but lim x→7 f(x) is not equal to 0.
False. Divison by zero is not allowed.
False. There is not enough information given to determine lim x→7 f(x)/g(x)
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