Chapter 1: Q. 12 (page 97)

Sketch a labeled graph that illustrates what is going on in the proof of Theorem 1.6 in the reading. Your graph should include two different $ϵ$ -bars and a graphical reason that they cannot overlap.

Short Answer

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Step by step solution

Step 1. Given information.

We have to sketch a labeled graph that illustrates what is going on in the proof of Theorem 1.6 in the reading.

Step 2. Sketch the graph.

Theorem 1.6 says that for a limit to exist, if $lim_{x \to c} f (x) = L and lim_{x \to c} f (x) = M,then L = M .$

For the first limit expression $lim_{x \to c} f (x) = L$ , the graph is

For the second limit expression the graph is :

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Sketch a labeled graph that illustrates what is going on in the proof of Theorem 1.6 in the reading. Your graph should include two different $ϵ$ -bars and a graphical reason that they cannot overlap.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Sketch the graph.

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Sketch a labeled graph that illustrates what is going on in the proof of Theorem 1.6 in the reading. Your graph should include two different ϵ-bars and a graphical reason that they cannot overlap.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Sketch the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Probability and Statistics

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Sketch a labeled graph that illustrates what is going on in the proof of Theorem 1.6 in the reading. Your graph should include two different $ϵ$ -bars and a graphical reason that they cannot overlap.