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Q. 12

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Found in: Page 119

### Calculus

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

# 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. $\underset{x\to {2}^{-}}{\mathrm{lim}}f\left(x\right)=-\infty ,\underset{x\to {2}^{+}}{\mathrm{lim}}f\left(x\right)=\infty ,f\left(2\right)=3.$

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

The graph of f is

See the step by step solution

## Step 1. Given Information.

The given function is $\underset{x\to {2}^{-}}{\mathrm{lim}}f\left(x\right)=-\infty ,\underset{x\to {2}^{+}}{\mathrm{lim}}f\left(x\right)=\infty ,f\left(2\right)=3.$

## Step 2. Describing the discontinuity.

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

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

There is not any one-sided continuity at $x=2$ because $\underset{x\to {2}^{-}}{\mathrm{lim}}\ne f\left(2\right)\mathrm{and}\underset{\mathrm{x}\to {2}^{+}}{\mathrm{lim}}\ne \mathrm{f}\left(2\right).$

## Step 4. Graph of f.

The graph of f is