We will solve 2 different exponential equations: x^2*e^x=2 and x+e^x=2 by using the Lambert W function.
Lambert W function Intro: https://youtu.be/sWgNCra93D8
Solve x*e^x=1 by using Newton's Method, https://youtu.be/EjUp_5X6io4
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We know i^0=1 but what is 0^i? In fact, it turns out 0 to the i-th power is another undefined expression. This is a very interesting complex analysis topic. Whenever we have a real number raised to a complex power, things might get strange. If you find math…

If a ball's velocity always equals exactly its position, how long will it take to reach x = 10, if it starts at x = 1?Thanks to Kaan and Fatih Ulupinar for suggesting this problem!

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Programa de Doutorado: Geometria Algébrica I - Aula 22 Professor: Roberto Mikhail Verbitskiy Aulas anteriores: https://goo.gl/pq2Y8Y Variedades afins e proje...

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Integral of e^x^2 using the Imaginary Error Function!
The "real" version: https://youtu.be/jkytxdedxhU

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In this video, I give a proof of the celebrated l'Hopital's rule in calculus, which is a very useful tool to calculate limits. It is actually one of my favorite proofs, because it illustrates the beauty and elegance of analysis. Enjoy!

I also get interrupted…