Exercise 1: Precise Definition of a Vector Function Limit

In this video I go over the precise definition of a vector function limit and prove it in 2 different ways. The 1st solution involves assuming the vector exists, and then using the basic definition of a vector function limit as well as the 3D distance formula, to prove the difference inequalities of the precise definition. The 2nd solution is the reverse: it involves assuming the precise definition difference inequalities and then working backwards to prove the vector function limit exists. Lastly, I show that the precise definition of a vector function limit in 3D can be visualized as a sphere which gets indefinitely smaller as the interval shrinks. YouTube - Summary - Notes - Playlist - Vector Functions playlist

This is probably the only in-depth precise definition of limits for vector functions anywhere in the internet, so buckle up!

#math #vectorfunctions #limits #science #calculus

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