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Q. 10

Found in: Page 119


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Each function in Exercises 9–12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx2-f(x)=2, limx2+f(x)=1, f(2)=1.

The type of discontinuity is a jump discontinuity and f(x) is right continuous at x=2.

The graph of f is

See the step by step solution

Step by Step Solution

Step 1. Given Information. 

The given function is limx2-f(x)=2, limx2+f(x)=1, f(2)=1.

Step 2. Describing the discontinuity. 

From the function, we can depict that limx2-f(x)=2 and limx2+f(x)=1 both exist but are not equal to f(2)=1.

Thus, f(x) has a jump discontinuity at x=2.

Step 3. Describing one-sided continuity at x=c.

The f(x) is right continuous at x=2 but not left continuous because limx2+f(x)=f(2).

Step 4. Graph of f.

The graph of f is

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