# High School Math : Calculating Limits

## Example Questions

### Example Question #5 : Calculus I — Derivatives

Calculate  .

The limit does not exist.

Explanation:

Substitute  to rewrite this limit in terms of u instead of x. Multiply the top and bottom of the fraction by 2 in order to make this substitution:

(Note that as .)

, so

, which is therefore the correct answer choice.

### Example Question #1 : Calculating Limits

Calculate

The limit does not exist.

Explanation:

You can substitute  to write this as:

Note that as

, since the fraction becomes indeterminate, we need to take the derivative of both the top and bottom of the fraction.

, which is the correct choice.