Convergence of the Taylor Series of sin(x)

[@InspirationIsFree]

Thank you! This really cleared up a lot of things for me - i didn't really know what convergence meant after learning taylor polynomials and this makes it clear that it's concerned with whether the approximation eventually becomes identical to the function. I've subscribed and I hope you keep making math videos!

[@JCCCmath]

Glad the video helped. Let me know if there is anything else that should be added.

[@adityaprasad465]

@@JCCCmath Thanks for an awesome video! One thing that might be useful: a real analytic function is one that equals its Taylor series in a neighborhood of every point. This is easy to confuse with the idea that the Taylor series converges to the function everywhere (as with sine). It could be worthwhile to explain the difference.

[@izzygrandic]

This is a great video and you are a great teacher.

[@JCCCmath]

Thank you. Glad you liked it.

[@lel4159]

Thank you for the video. I think there is a small mistake in the first formula though: it is "n" instead of "n+1" in the exponent of (-1). Best regards

[@JCCCmath]

Good catch. I fixed that in the version I use internally for my classes, but have not fixed it here. I will add something in the description.

[@kartik303]

Thank you sir

[@dume85]

your backwards handwriting is amazing

[@fadybitar6433]

he doesn't write backwards lmaooo.. he simple writes the normal way and then flips the image

[@dume85]

@@fadybitar6433 nah you're just jealous that you can write backwards with your left hand like that.

[@barancel11]

it is a very good explanation indeed, however it is too trivial. a more difficult problem could be used. thankss

[@JCCCmath]

Typically in our Integral Calculus course we focus on e^x, sin(x), cos(x), and the binomial series for our applications, so that is why I proved sin(x) and e^x. We usually leave the convergence of the others to exercises, so I i didn't want to spoil that. Glad you enjoyed.