#### Estimating Limits

Estimating Limits is just plugging numbers into a function and seeing what happens! The trick is picking the right numbers to plug in, but even that is easy.

#### Example

$\displaystyle\lim_{x \to 5}\frac{x^2-25}{x-5}$

Since $x$ is approaching 5 we need to pick numbers that are close to 5. We also need to make sure:

- The numbers are getting closer to 5
- Some numbers are smaller than 5 and some numbers are bigger than 5.

Let's pick 4.9, 4.99, 4.999, 5.1, 5.01, 5.001.

Now we just plug the numbers into our function:

$x$ | 4.9 | 4.99 | 4.999 | 5.001 | 5.01 | 5.1 |

$f(x)$ | 9.9 | 9.99 | 9.999 | 10.001 | 10.01 | 10.1 |

Note how the table is organized. As $x$ values approach 5 (in the center) we can see that the $f(x)$ values approach 10. So we estimate that:

$\displaystyle\lim_{x \to 5}\frac{x^2-25}{x-5} = 10$

#### Questions

Please post your questions about this video in our HW Help Forum

#### Mistakes

If you found a mistake in this video please email us at feedback@rootmath.org