**Problem Statement:**Suppose \( f, g \) are real-valued functions on \( E \subset \mathbb{R} \) and \( p \) is a limit point of \( E \). If \( g \) is bounded on \( E \) and \( \lim_{x \to p} f(x) = 0 \), show that\[\lim_{x \to p} f(x)g(x) = 0.\]

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Answered: Suppose f, g are real-valued functions…

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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Suppose f, g are real-valued functions on ECR and p is a limit point of E. If g is bounded on E and lim f(x) = 0, show that x-p lim f(x)g(x) = 0. x-p