Problems 1-3: always necessarily true. If possible, provide an example to support your statements. Be horough in your explanations. ,Explain why the following statements, in your own words, are not 1. If f(1) > 0 and f(3) < 0, then there exists a value x = c in the interval (1,3) such that f(c) = 0. 2. lim 2+4x-5 x-1x2+3x-4 lim x²+4x-5 lim x2+3x-4 3. If lim f(x) = ∞ and lim g(x) = ∞ , then lim [f(x) – g(x)] = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problems 1-3:
Explain why the following statements, in your own words, are not
always necessarily true. If possible, provide an example to support your statements. Be
thorough in your explanations.
1. If f(1) > 0 and f (3) < 0, then there exists a value x = c in the interval (1, 3) such that
f(c) = 0.
2. lim *2+4x-5
x+1 x2+3x-4
lim x2+4x-5
lim x2+3x-4
x-1
3. If lim f (x) = ∞ and lim g(x) = ∞ , then lim [f (x) – g(x)] = 0
%3D
%3D
Transcribed Image Text:Problems 1-3: Explain why the following statements, in your own words, are not always necessarily true. If possible, provide an example to support your statements. Be thorough in your explanations. 1. If f(1) > 0 and f (3) < 0, then there exists a value x = c in the interval (1, 3) such that f(c) = 0. 2. lim *2+4x-5 x+1 x2+3x-4 lim x2+4x-5 lim x2+3x-4 x-1 3. If lim f (x) = ∞ and lim g(x) = ∞ , then lim [f (x) – g(x)] = 0 %3D %3D
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