Taylor's Theorem, proof

A proof for Taylor's Theorem, which states that f(x) can be represented as the sum of a sequence of derivatives.

Category:

Education

Tags:

• math
• mathematics
• calculus
• integration
• taylor's
• theorem
• series
• sequences

[PeetPb]

I'm sorry but I'm a lil bit curious ... what the HELL happend at 1:28 ?

[jehan60188]

@PeetPb i don't know what you mean. I used a fade to demonstrate that a new term was written.

[jehan60188]

@PeetPb use integration by parts

u = t and dv = f''

[jehan60188]

@PeetPb use integration by parts

u = t and dv = f''

[Flashylightsmeow]

This video is awful

[jehan60188]

@Flashylightsmeow thank you for the feedback, I am always happy to accept constructive criticism

[MarcusAntoni]

You just showed that the theorem hold for any finite n in the Positive integers, induction does not prove it works for infinity. Your induction only proves the taylor polynomial theorem. Unless you did something I didn't see.

[PeetPb]

@jehan60188 I still somehow cannot figure it out .. I made another iteration of integraton by parts on that integral(tf''(t)dt) as u=t and v=f'(t) du=dt dv=f''(t)dt so the integral is equal to tf'(t)-integral f'(t)dt ... and now the integral vanishes and leaves me a useless equation f(x)-f(a)=xf'(x)-af'(a) ... I'm starting to be despaired, where have I made a mistake ?

[PeetPb]

@jehan60188 I know ... I just can't work out what u have done there ... you calculated the integral f'(t)dt so it is eq. to f'(t)t-int t f''(t) dt (all that evaluated between a and x) and than ? how could you factor out f'(a) at that first term ? and how did you "pull" that x into the integral ?

[MrCbaucke]

thanks for putting this up - nice clear explanation. Hadn't looked at the proof for 25 years - great reminder...

[cheatcomp07]

@jehan60188 the problem is, you are writing something else and speaking something else.

[Flashylightsmeow]

Here's some, go die.