Discrete Math Let \( X \) be the space of positive continuous functions. Define the relation \( R \) on \( X \) if for functions \( f, g, fRg \) if \[\lim_{x \to \infty} \frac{f(x)}{g(x)} = L \]where \( L \) is a number not equal to 0.(a) Show that this is an equivalence relationship.(b) Show that \( f(n) = n^2 \) and \( g(n) = n \ln n \) are NOT equivalent.

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Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

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Let X be the space of positive continuous functions. Define the relation R on X if for f(x) functions f, g, fRg if lim = L where L is a number not equal to 0. x→∞ g(x) (a) Show that this is an equivalence relationship. (b) Show that f(n) = n² and g(n) = n ln n are NOT equivalent.