Question

Determine whether the function is continuous or discontinuous:

If discontinuous, identify the type of discontinuity:

(If a function is continuous for type write none.)

f (x)= x+1/x

Answer 1

The function is discontinuous ad x=0

It has an infinite discontinuity

Explanation:

First we need to take a look at the domain. We can see that the function is not defined for x=0. So next we need to determine how the function behaves around x=0, so we can find the lateral limits:

`\lim_(x \to 0^-) (x+1)/(x) = - \infty`

`\lim_(x \to 0^+) (x+1)/(x) = \infty`

You can calculate these limits by using tables and values close to 0 from the left and from the right.

We can see that the function approaches -infinity as it approaches zero from the left and it approaches positive infinicty as it approches to zero from the right. Therefore it has an infinite discontinuity.

This discontinuity can be seen in the attached graph.