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.
$\lim_{x \to 2^{-}} f (x) = 2, \lim_{x \to 2^{+}} f (x) = 1, f (2) = 1 .$

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

The graph of f is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The given function is $\lim_{x \to 2^{-}} f (x) = 2, \lim_{x \to 2^{+}} f (x) = 1, f (2) = 1 .$

Step 2. Describing the discontinuity.

From the function, we can depict that $\lim_{x \to 2^{-}} f (x) = 2 and \lim_{x \to 2^{+}} f (x) = 1$ 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 $\lim_{x \to 2^{+}} f (x) = f (2) .$

Step 4. Graph of f.

The graph of f is

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Calculus

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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.
$\lim_{x \to 2^{-}} f (x) = 2, \lim_{x \to 2^{+}} f (x) = 1, f (2) = 1 .$

Step by Step Solution

Step 1. Given Information.

Step 2. Describing the discontinuity.

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

Step 4. Graph of f.

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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. limx→2-f(x)=2, limx→2+f(x)=1, f(2)=1.

Step by Step Solution

Step 1. Given Information.

Step 2. Describing the discontinuity.

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

Step 4. Graph of f.

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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.
$\lim_{x \to 2^{-}} f (x) = 2, \lim_{x \to 2^{+}} f (x) = 1, f (2) = 1 .$