Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
**Problem Statement:** Determine a condition on \(|x-4|\) that will assure that \(|\sqrt{x} - 2| < 0.01\). --- **Explanation for Educational Context:** In this problem, we are given an expression involving an absolute value and a square root. Our goal is to find a condition on \(|x-4|\) which will ensure that the expression \(|\sqrt{x} - 2|\) is less than 0.01. Such problems often involve concepts from calculus and analysis, particularly limits and continuity. Before proceeding with calculations, consider any constraints on \(x\) due to the square root (i.e., \(x \geq 0\)), and use properties of absolute values to simplify or manipulate the expressions involved.
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Transcribed Image Text:**Problem Statement:** Determine a condition on \(|x-4|\) that will assure that \(|\sqrt{x} - 2| < 0.01\). --- **Explanation for Educational Context:** In this problem, we are given an expression involving an absolute value and a square root. Our goal is to find a condition on \(|x-4|\) which will ensure that the expression \(|\sqrt{x} - 2|\) is less than 0.01. Such problems often involve concepts from calculus and analysis, particularly limits and continuity. Before proceeding with calculations, consider any constraints on \(x\) due to the square root (i.e., \(x \geq 0\)), and use properties of absolute values to simplify or manipulate the expressions involved.
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