please help with this question..

First, it is given that f(x) is a differentiable function.

and

Then, I have to prove by MI that

I don' t understand how to prove it :confused: . please help~

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- August 20th 2006, 05:44 PMling_c_0202prove by MI that
please help with this question..

First, it is given that f(x) is a differentiable function.

and

Then, I have to prove by MI that

I don' t understand how to prove it :confused: . please help~ - August 20th 2006, 05:55 PMThePerfectHackerQuote:

Originally Posted by**ling_c_0202**

Proof (by induction) that,

=

Then,

Then by the theorem before the derivative is,

- n times. But each summand can be reduced to, n-times. Thus,

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Keep you Calculus question in Calculus section :mad:

-=USER WARNED=- - August 20th 2006, 09:19 PMCaptainBlackQuote:

Originally Posted by**ling_c_0202**

Quote:

Then, I have to prove by MI that

Now (using the product rule):

So applying the supposition to the first term:

Which is the required result for .

So if we assume the required result for some , it is true for , hence

with the base case the result is proven by Mathematical Induction for all

(note we could have taken as the base case - which is trivialy true -

then the proof would apply for all ).

RonL - August 21st 2006, 07:55 AMling_c_0202thank you
Thank you very much!

I found that i got a mistake when i apply the product rule... stupid me :p