Taylor Series Expansion

#breakthroughjuniorchallenge
There are many ways to which you can expand a function using infinite series like Fourier Series, Dirichlet Series and a lot more. Taylor Series Expansion is one of the ways to expand a function "locally" in the form of infinite power series. To explain it in simple terms, you have a non-polynomial function and then you want to write it in form of polynomial because it is very easy to deal with yet accurate to some extent. Let's say for example, e to the x (e^x) how do you find e^0.24? Well, this is where Taylor Series Expansion comes in. We expand the function around a point of known value, for example, at x equals 0 which is (0,e^0) = (0,1). As we increase the degree of our polynomial or increase the degree of our Taylor Series, we are going to get a more precise approximation of the function. If the point is near or close to the point which we expand then we're going to need just a few terms to get a valid answer and if it's further away then we're going to need more terms. Expanding a function with Taylor Series isn't mandatory to add up to infinite terms, we just need only n terms if that expansion covers our point of interest already. So long story short, expanding a function closer to our point of interest will be less tiresome for us to find the value of the function at that point. P.S. This video is highly inspired by 3b1b and Morphocular
**A little more explanation on the word "locally" : because we are expanding the function at the point with known value which means we are using local information to get a function globally. Doesn't sound logical right? So there are possibilities that some functions can't be expand by Taylor Series and we call those functions "Non-analytic functions"
If you want to dive deeper - have a look at "Taylor's Theorem" and "Analytic functions"
TLDR : You have a non polynomial function. You want to get approximate the function at hard values to evaluate. You use Taylor Series Expansion. You get an accurate answer. 🥳🥳🥳

[@KiwiRedstone]

Nice video! Orz orz orz

[@watsanakanoknorranarttraku4156]

Orz Orz Orz

[@sleepntsheep1169]

🎉🤡🎉🎉? ?🎉🎉🎉🎉✔️ cool!!!!!! 0:04

[@kinari036]

Another cool!! video on Convex Hull : czcams.com/video/B06sS-HSQq4/video.htmlsi=pp12AtflXFRLJ7pV

[@OhNiceVal]

This vid is better than your table tennis skill 🎉

[@lastshottv7992]

Where is sourdough bro