Big-O Notation with Taylor Series

[@ahmed-xj8hp]

makes so much more sense than the convoluted lecture notes of my professor. Thank you, you’re a life saver

[@ibuprofencompactor]

dude I love you. Very clear video, thanks!

[@aldoaguilar8597]

Great video!

[@nguyendieu8141]

thanks, great video

[@zarekhunter2506]

Awesome! Extremely helpful video!

[@p_square]

great video! helped a lot

[@julianpbt7942]

You are a hero!!!

[@xtosu9643]

I literally searched for fucking hours to figure out my answer AND IT WAS JUST LONG FUCKING DIVISION TYSM

[@jorgitusnone3587]

Great videos! You mention "Notes: 144 to 151", are those notes available for download? Thanks in advance!

[@MinhBui-h4x]

I’m sorry, but why the (n + 1)st order derivative of f has to be bounded for all z between x node and x? Could you explain more? It’s seemingly true as that is the Taylor polynomial for. I think we have to assume something more.

[@mathemation]

The result being used here is Taylor's inequality, which comes from Taylor's remainder theorem. Taylor's remainder theorem tells us that the error in the nth order approximation is an integral involving the (n+1)th derivative. By bounding this derivative on the interval of interest, we can evaluate the integral to bound the error in our approximation. This is Taylor' inequality. You may want to check out my videos on these topics for more info: Taylor's Remainder Theorem: kzbin.info/www/bejne/gYCli5eshteGq68&ab_channel=Mathemation Taylor's Inequality: kzbin.info/www/bejne/b5aTh4ppeLyqb7c&ab_channel=Mathemation

[@MinhBui-h4x]

@@mathemation ok, thanks. Btw , what app do you use to write down things in your videos?

[@mathemation]

I record the videos on an iPad using the app Explain Everything. I like it because it allows you to edit videos within the app, though some of the editing features are limited.