In my earlier video I went over the precise definition of infinite limits and in this video I illustrate it further by going over a useful example. The example I go over is trying to prove that the limit as x approaches 0 of 1/x² is infinite. Intuitively, it is easy to see why the limit is true but proving according to the precise definition is a bit more abstract but once you fully grasp the precise definition, proofs like this should be pretty straight forward.

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Infinite Limits – Precise Definition - Example

Recap on Definition

Let f be a function defined on some open interval that contains the number a, except possibly at a itself. Then:

Means that for every positive number M there is a positive number δ such that:

Example

Solution