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Q. 23

Expert-verifiedFound in: Page 120

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

For each function *f* graphed in Exercises *23–26*, describe the intervals on which *f* is continuous. For each discontinuity of *f*, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

The function is continuous on the interval $\left(-\infty ,2\right)\cup \left(2,\infty \right)$ and it has a removable discontinuity and there is not any one-sided continuity.

The given graph is

From the graph, we can depict that the graph is continuous on the interval $\left(-\infty ,2\right)\cup \left(2,\infty \right).$

From the graph, we can depict that it has removable discontinuity because $\underset{x\to 2}{\mathrm{lim}}f\left(x\right)$ exists but it is not equal to $f\left(2\right).$

The graph is neither left continuous nor right continuous at $x=2.$

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