Suggested languages for you:

Americas

Europe

Q. 12

Expert-verifiedFound in: Page 119

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

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

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.

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

The graph of *f *is

94% of StudySmarter users get better grades.

Sign up for free