Question

Exercise 4.2.4. Consider the reasonable but erroneous claim that \\ $\lim_{x \to 10} 1/||x|| = 1/10$. \\ (a) Find the largest $\delta$ that represents a proper response to the challenge of \\ $\epsilon = 1/2$. \\ (b) Find the largest $\delta$ that represents a proper response to $\epsilon = 1/50$. \\ (c) Find the largest $\epsilon$ challenge for which there is no suitable $\delta$ response \\ possible.

          Exercise 4.2.4. Consider the reasonable but erroneous claim that \\
$\lim_{x \to 10} 1/||x|| = 1/10$. \\
(a) Find the largest $\delta$ that represents a proper response to the challenge of \\
$\epsilon = 1/2$. \\
(b) Find the largest $\delta$ that represents a proper response to $\epsilon = 1/50$. \\
(c) Find the largest $\epsilon$ challenge for which there is no suitable $\delta$ response \\
possible.

Exercise 4.2.4. Consider the reasonable but erroneous claim that

limx → 10 1/||x|| = 1/10.

(a) Find the largest δ that represents a proper response to the challenge of

ϵ = 1/2.

(b) Find the largest δ that represents a proper response to ϵ = 1/50.

(c) Find the largest ϵ challenge for which there is no suitable δ response

possible.

Added by Chloe M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kirsty Gledhill

01/08/2024

Step 1

Step 1: The limit does not exist because the function oscillates between 1/9 and 1/10 as x approaches 10. Show more…

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Exercise 4.2.4. Consider the reasonable but erroneous claim that $$\lim_{x \to 10} \frac{1}{[[x]]} = \frac{1}{10}.$$ (a) Find the largest $\delta$ that represents a proper response to the challenge of $\epsilon = 1/2$. (b) Find the largest $\delta$ that represents a proper response to $\epsilon = 1/50$. (c) Find the largest $\epsilon$ challenge for which there is no suitable $\delta$ response possible.