https://youtu.be/L9jrwf-IKeU

In this video I go over briefly what the direct substitution property is for limits and also go over a very useful example on how to solve limits where you can't directly substitute numbers into the limit.

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# Limits– Where Direct Substitution Doesn’t work

![Limits - Where Direct substitution doesn't work.jpg](https://files.peakd.com/file/peakd-hive/mes/Eo8SuXCZvpSYvbqcYDgowVi7rAmeQaLYvT33nub8SRnCyMia9b6v11wKGPCFeVQDWQC.jpg)
	
## Direct Substitution Property

If f is a polynomial or a rational function and a is in the domain of f, then:

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tw9yBHVZBF8b4kUSk17vwEdpkEeUsKNrYpTnZpqRbdFx712Zu4oVRhGsQMCi8ExgJYL.png)

Functions with the Direct Substitution Property are called continuous at a. 

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eo6S6U3zhHba3f7fvStGDi8FJNSuJCMMXdS5AzXdWWJxxoMVnPQspjcy5c5RFb6E5Mv.png)

## Where Direct Substitution Does Not Work 

Not all limits can be evaluated by direct substitution, such as the following example:

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ym9Ybjq4hin1MquGPwqBEkYdccfBZcey3HJi8HBDCiY5Lrbg4MgDtwUmYyRJuS.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ym7bk2ByXpEFCuwrh63VFJ78t9g5cFD2kbq9EHpyq7ZS4Tzx6hYyG4wtqjosSc.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8CfKPvnnfJh4QfFJbSpP7gQJk6cJLBUmLUft6tRHfWp5JtjayYcp8triXsQkggajrk.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8CfKPvxwpPfLZYYG1qabcC24NdA8Mpb8rrTaWzWfnugDywSqX9DDRxhLuyhcK6wXG8.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8DBnQFPMKyDuNqZYxYkXGTGMnSqFk5bQfefWY38xWWvNKBHYqpqv2W3e2b4gVce3Ze.png)