https://youtu.be/IECI8QpGkzY

In my earlier video, I went over the precise definition of one sided limits and in this video I go over a useful example to show how you can prove the limit of a function using the precise definition. Make sure to also watch my videos on the general precise definition of limits and the examples on it in the video links below.

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- YouTube: [https://youtu.be/IECI8QpGkzY](https://youtu.be/IECI8QpGkzY)

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# Precise Definition of One Sided Limits – Example

![Precise Definition of a One Sided Limit Example.jpg](https://files.peakd.com/file/peakd-hive/mes/454FFaaH-Precise20Definition20of20a20One20Sided20Limit20Example.jpg)
	
## Precise Definition of Left Hand Limit

![image.png](https://files.peakd.com/file/peakd-hive/mes/PB90eatW-image.png)

If for every number ε>0 there is a number δ>0 such that:

![image.png](https://files.peakd.com/file/peakd-hive/mes/79X9YzcF-image.png)

Precise Definition of Right Hand Limit:

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

If for every number ε>0 there is a number δ>0 such that:

![image.png](https://files.peakd.com/file/peakd-hive/mes/FZthL5AB-image.png)

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## Example

![image.png](https://files.peakd.com/file/peakd-hive/mes/5Cu88P4Q-image.png)

### Solution

![image.png](https://files.peakd.com/file/peakd-hive/mes/7Tlsk9fn-image.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/mL6mH4Ve-image.png)