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Mathematical Proof. | Using the Epsilon-Delta definition we are going to prove that the limit for the given function is 4. | Real Analysis & Multi-variable Calculus. by paultactico2

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· @paultactico2 · (edited)
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Mathematical Proof. | Using the Epsilon-Delta definition we are going to prove that the limit for the given function is 4. | Real Analysis & Multi-variable Calculus.
![portada epsilon delta.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23xAPE3CYnfou55e6ekvBbrzvhdBcsp5E9LbTVdsMZwb3WLqXyXGWoKtma91NDRrEYtui.jpg)

# Personal presentation.

> **Hello everyone, receive a cordial greeting from me. I am a young mathematician apprentice, Venezuelan and enthusiastic about science in general. At present I am pursuing a "degree in mathematics" career, in which I am in the middle of the degree. On the other hand, I am currently doing research in the area of number theory at the University of Carabobo (UC).**

Well, with great pleasure I will be uploading math content, tips to increase your performance in the study and science in general.

I hope you will accompany me on the arduous but beautiful path of mathematics and science.

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Today i will prove that the limit for the given f(x,y) is 4, using the Epsilon-delta definition for it. Also i will show you how to use the Distance Formula in order to find the necessary relations between epsilon-delta. At the end you will see how i found the proper epsilon to satisfy the epsilon-delta definition of ordinary limit and prove that the limit is L, that in this case of study is 4. This mathematical proof belongs to the areas of: Real Analysis and Multi-variable Calculus. 

![barra espaciadora.jpg](https://images.hive.blog/DQmbPvQiC3wfiFuWTQ52bAqL2ysrrVjTjxf4Je8d8t4GSEM/barra%20espaciadora.jpg)

 Next I proceed to carry out the mathematical proof about the Limit on question.

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![barra espaciadora.jpg](https://images.hive.blog/DQmbPvQiC3wfiFuWTQ52bAqL2ysrrVjTjxf4Je8d8t4GSEM/barra%20espaciadora.jpg)

<center>  **The Limit to prove.**  </center>

![enunciado.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23tmmf8kQENJurLozpiZVQMDbo8p4uGGCNATj42dB19fBJaRxxG4sFnqomJCPuRmhBfeU.jpg)

![barra espaciadora.jpg](https://images.hive.blog/DQmbPvQiC3wfiFuWTQ52bAqL2ysrrVjTjxf4Je8d8t4GSEM/barra%20espaciadora.jpg)

<center> **Necessary definitions to deal with the mathematical proof.**</center>


![Definiciones necesarias..jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23tHb6m7ho9NQXBcx8wvGq9BpDEoBpEnX7R22Zg3mvr3UgTDgxaxaox691YsNNxbQgevg.jpg)

![barra espaciadora.jpg](https://images.hive.blog/DQmbPvQiC3wfiFuWTQ52bAqL2ysrrVjTjxf4Je8d8t4GSEM/barra%20espaciadora.jpg)

<center> **The Hand-made mathematical proof.** </center>


![delta 001.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23sxpRyYsZYk62JNRo5hUG7PAGa1WGQ58ryxmuLhm55WFg3QjwPXdtzqZULQy7gBwNej6.jpg)

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![delta 002.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23twAKUfrpq2dWbkhFeCV7NvJ6W686R8WCBM6yM4egAjjCdwCoaj7MSuiKmi5CMockjwS.jpg)

![barra espaciadora.jpg](https://images.hive.blog/DQmbPvQiC3wfiFuWTQ52bAqL2ysrrVjTjxf4Je8d8t4GSEM/barra%20espaciadora.jpg)

<center> **Mathematical proof written in LaTex.** </center> 

<center> **LaTex Sheet N°1.** </center>


![sheet 1.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23tHb6kphqavzSbguLuLQex2YdwVYTaeWxfKTUJgk3VKXDomDMjqz5TqxxE4npEwoG6qS.jpg)

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![sheet 2.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23tHbr9ykz8JQ9m6EdZg2XL3fpUchUK77YozLYt49SpRhaBur1Sd6ELg59vcyn1D66AEQ.jpg)

![barra espaciadora.jpg](https://images.hive.blog/DQmbPvQiC3wfiFuWTQ52bAqL2ysrrVjTjxf4Je8d8t4GSEM/barra%20espaciadora.jpg)

<center> **In case you missed something** </center> 


![Clarification1.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23sxozx9nSSn71MNxXxTdGSuwrpm5SWZyffi3y5UavSz9qybtvZsoqghUg77b5B7wpvJY.jpg)

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![Clarification 2.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23t8CfKjGpMggqxnYdkeMaVZ5fYeU7FFwdUa4NFdVnZTQbTfEc2j6YDZRLUdGhiHek4pC.jpg)

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![clarification 3.jpg](https://files.peakd.com/file/peakd-hive/paultactico2/23t8CfKjJLp9g2KnNofkAxLjyTDGeHGVKYUniWKLQDCkWbyDQiz6Qt3WPDyraBPVJcnaG.jpg)


![linea prueba 3 mejorada.jpg](https://images.hive.blog/DQmdJGJk3WB5TZ3tYMNfSKMKdCRdh9qQd9mnTRJcEBwA9Mm/linea%20prueba%203%20mejorada.jpg)

The Hand-made mathematical proof and the LaTex written sheets were made it by me:  [@paultactico2](https://hive.blog/@paultactico2)


![gif matematicas.gif](https://files.peakd.com/file/peakd-hive/paultactico2/23wWrWwKaKMRYiq6yUuR3ZJSsC8LDgkhev6SQ2M1WAT9GAAdj138ghrczi6S285LS88Qk.gif)


![linea prueba 3 mejorada.jpg](https://images.hive.blog/DQmdJGJk3WB5TZ3tYMNfSKMKdCRdh9qQd9mnTRJcEBwA9Mm/linea%20prueba%203%20mejorada.jpg)
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vote details (237)
@poshbot ·
https://twitter.com/paultacticoofi/status/1369524896506724357
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@steemstem ·
re-paultactico2-mathematical-proof-or-using-the-epsilon-delta-definition-we-are-going-to-prove-that-the-limit-for-the-given-function-is-4-or-r-20210310t203828780z
<div class='text-justify'> <div class='pull-left'>
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vote details (1)
@paultactico2 ·
Thank you for your support,fellows. I already approved your witness and delegated some hp too (y)
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