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Let f and g be continuous functions from R to R. Define the set C {x €R: f(x)=g(x)}. If (x,) is a sequence in C and x = lim(x,), show that x EC.

Let f and g be continuous functions from R to R. Define the set C {x €R: f(x)=g(x)}. If (x,) is a sequence in C and x = lim(x,), show that x EC.

Advanced Engineering Mathematics
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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Let f and g be continuous functions from R to R. Define the set C= {x €R: f(x)=g(x)}. If (x,) is a sequence in C and x = lim(x,), show that x €C.
Transcribed Image Text:Let f and g be continuous functions from R to R. Define the set C= {x €R: f(x)=g(x)}. If (x,) is a sequence in C and x = lim(x,), show that x €C.
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