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Exercise 1: Precise Definition of a Vector Function Limit by mes

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hive-111030 · @mes ·
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Exercise 1: Precise Definition of a Vector Function Limit
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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](https://youtu.be/mVJ4wviwDs8) - [Summary](https://inleo.io/threads/view/mes/re-leothreads-2bsgqbqqj) - [Notes](https://peakd.com/hive-128780/@mes/omhbcxkw) - [Playlist](https://www.youtube.com/playlist?list=PLai3U8-WIK0GwdMY-E9_4LsmYmO-IxcoX) - [Vector Functions playlist](https://www.youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U)

**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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For the best experience view this post on [Liketu](https://liketu.com/@mes/exercise-1-precise-definition-of-a-vector-function-limit)
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