f(x) (4) lim x-c g(x) L M provided M0 and g(x) #0 for any a E

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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Prove (4) using the result of Theorem 5.3

(4) lim
x-c
f(x) L
M
g(x)
=
provided M 0 and g(x) ‡0 for any x € A.
Transcribed Image Text:(4) lim x-c f(x) L M g(x) = provided M 0 and g(x) ‡0 for any x € A.
x-C
THEOREM 5.3. Suppose that A CR, f: A → R, and c is a limit point of A. Then lim f(x) = Lif
and only if, for every sequence (an)
A for which each an c and an →c, we have f(an) → L.
Transcribed Image Text:x-C THEOREM 5.3. Suppose that A CR, f: A → R, and c is a limit point of A. Then lim f(x) = Lif and only if, for every sequence (an) A for which each an c and an →c, we have f(an) → L.
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