# Limits of functions

The **limit of function f as x approaches c is L** if f(x) can be made to be as close to L as desired by making x sufficiently close to c. Otherwise:

We write:

For example:

because:

You can't always find the same limit when you approach from both sides, that’s why we define the lateral or one-sided limits:

- The **limit of a function f as x approaches c from the left** is L^{-} if f(x) can be made to be as close to L^{-} as desired by making x sufficiently close to c from below:

- The **limit of a function f as x approaches c from the right** is L^{+} if f(x) can be made to be as close to L^{+} as desired by making x sufficiently close to c from above:

For example:

Then, the function has a limit on c if and only if the one-side limits exist and are equal:

Then, in the example

We have the same properties as in the sequences:

**Exercise**: calculate the limit of *f* as *x* approaches *-1, 2* and* 5,* if:

Solutions:

Licensed under the Creative Commons Attribution Non-commercial Share Alike 3.0 License