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Chapter 1: Q. 14 (page 97)

Suppose f is a function with f(2) = 5 where for all ϵ> 0, there is some δ > 0 such that if x ∈ (2 − δ, 2) ∪ (2, 2 + δ), then f(x) ∈ (3 − ϵ, 3 + ϵ). Sketch a possible graph of f.

Short Answer

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We have to sketch a graph of f where f is a function with f(2) = 5 where for all ϵ> 0, there is some δ > 0 such that if x ∈ (2 − δ, 2) ∪ (2, 2 + δ),

Step by step solution

01

Step 1. Given information.

We have to sketch a graph of f where f is a function with f(2) = 5 where for all ϵ> 0, there is some δ > 0 such that if x ∈ (2 − δ, 2) ∪ (2, 2 + δ),

02

Step 2. Sketch a graph.

One possible graph of given conditions is :

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