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Problem 2 True or false? Justify your answer. Give a counterexample if it is false. (a) If limx→a f(x) = 0 and limx→a 9(x) = 0, then lima ( does not exist. g(x) (b) If neither limx→a f(x) nor limx→a g(x) exists, then limx→a (f(x) + g(x)) does not exist. (c) If limx→a f(x) exists, but limx→a g(x) does not exist, then limx→a (f(x) + g(x)) does not exist. (d) If limx→a (f(x)g(x)) exists, then the limit must be equal to f(a)g(a). (e) If limx→a f(x) = ∞ and limx→a 9(x) = ∞, then limx→a (f(x) − g(x)) = 0.

Problem 2 True or false? Justify your answer. Give a counterexample if it is false. (a) If limx→a f(x) = 0 and limx→a 9(x) = 0, then lima ( does not exist. g(x) (b) If neither limx→a f(x) nor limx→a g(x) exists, then limx→a (f(x) + g(x)) does not exist. (c) If limx→a f(x) exists, but limx→a g(x) does not exist, then limx→a (f(x) + g(x)) does not exist. (d) If limx→a (f(x)g(x)) exists, then the limit must be equal to f(a)g(a). (e) If limx→a f(x) = ∞ and limx→a 9(x) = ∞, then limx→a (f(x) − g(x)) = 0.

Advanced Engineering Mathematics
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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Problem 2 True or false? Justify your answer. Give a counterexample if it is false. (a) If limx→a f(x) = 0 and limx→a g(x) = 0, then limx→a f(x) does not exist. g(x) (b) If neither limx→a f(x) nor limx→a g(x) exists, then limx→a (f(x) + g(x)) does not exist. (c) If limx→a f(x) exists, but limx→a g(x) does not exist, then limx→a (f(x) + g(x)) does not exist. (d) If limx→a (f(x)g(x)) exists, then the limit must be equal to f(a)g(a). (e) If limx→a f(x) = = ∞ and limx→a 9(x) = ∞, then limx→a (ƒ(x) − g(x)) = 0.
Transcribed Image Text:Problem 2 True or false? Justify your answer. Give a counterexample if it is false. (a) If limx→a f(x) = 0 and limx→a g(x) = 0, then limx→a f(x) does not exist. g(x) (b) If neither limx→a f(x) nor limx→a g(x) exists, then limx→a (f(x) + g(x)) does not exist. (c) If limx→a f(x) exists, but limx→a g(x) does not exist, then limx→a (f(x) + g(x)) does not exist. (d) If limx→a (f(x)g(x)) exists, then the limit must be equal to f(a)g(a). (e) If limx→a f(x) = = ∞ and limx→a 9(x) = ∞, then limx→a (ƒ(x) − g(x)) = 0.
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