Taylor / Maclaurin Series Expansion - Proof of the Formula

Taylor / Maclaurin Series Expansion - Deriving the Formula. In this video, I show how to find the Taylor series expansion for a function, assuming that one exists! It is nothing too heavy: we just take derivatives and plug in the value at which we are centering the function. I do not find any Taylor series of specific functions in this video, nor do I justify when a Taylor series expansion is valid (not all functions have power series expansion!).

Category:

Education

Tags:

• taylor
• series
• maclaurin
• expansion
• formula
• proof
• prove

[gremlinextreme101]

This is a derivation not a proof. We saw the proof when i was in BC calc, you have to use Cauchy's mean value theorem to show that for greater numbers of terms the difference between the summation and function gets as small as desired.

[patrickJMT]

@gremlinextreme101 as i said at the very beginning of the video, if a function has a power series representation, this is a proof of how to find its expansion. as i also pointed out, this does not justify that a function has a power series rep; to do that you can use taylor's inequality. thanks for pointing out what was said in the first minute of the video.

[unionbay8]

every one of your videos start with "alright"

:D

[patrickJMT]

@unionbay8 yes, sort of an annoying running joke at this point : )

[ceciliasmile]

Clear and understandable!!! Thank you Patrick!

[xXSabzzXx]

Thanks! Helped me a lot. Starting to get the hang of this now. This 1 video helped me understand more that a lecture and staring at my confusing notes!

[Acerz06]

nice one ! thnx !!

[Flashylightsmeow]

Superb video!

[gremlinextreme101]

@Budisawsome I'm a junior in applied math

[Budisawsome]

@patrickJMT Do I listen to the high school student or the Master's in mathematics... hmm such a tough one.

[tigerlilja1]

Wished I had this when I was in calc2....oh well

[regionalmathematiful]

@patrickJMT why not try "ok!"