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Q. 12

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Calculus

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.
$\lim_{x \to 2^{-}} f (x) = - \infty, \lim_{x \to 2^{+}} f (x) = \infty, f (2) = 3 .$

The type of discontinuity is an infinite discontinuity and there is not any one-sided continuity.

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 $\lim_{x \to 2^{-}} f (x) = - \infty, \lim_{x \to 2^{+}} f (x) = \infty, f (2) = 3 .$

Step 2. Describing the discontinuity.

From the function, we can depict that f(x) has infinite discontinuity because both of $\lim_{x \to 2^{-}} f (x) and \lim_{x \to 2^{+}} f (x)$ are infinite.

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

There is not any one-sided continuity at $x = 2$ because $\lim_{x \to 2^{-}} \neq f (2) and \lim_{x \to 2^{+}} \neq f (2) .$

Step 4. Graph of f.

The graph of f is

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