In this video I prove the Product Law which is the 4th Limit Law from my overview of Limit Laws video (see video link below). The Product Law states that the limit of a product is the product of limits. I prove this using the precise definition of a limit and although the proof may seem a bit abstract, it becomes much better to understand when you grasp fully the concept of the precise definition of a limit. So make sure to watch this video as well as the precise definition of a limit video (from the link below).
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Limit Laws – Proof of the Product Law
Law 4: Product Law
The limit of a product is the product of the limits.
Recap on Precise Definition of a Limit
If for every number ε > 0 there is a number δ > 0 such that:
Proof of Product Law