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Real Analysis

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QuantumJG:

--- Quote from: TrueTears on March 01, 2010, 09:43:07 pm ---if f has a power series expansion: then the maclaruin series is just a special case of it: namely, centered at 0. (a = 0)

but that's not the slick part, the coolest part is the relationship between the coefficients of the power series f(x) and the derivatives of f(x), thats the part i love the most!!

--- End quote ---

So what this is impliying that if,





So

  becomes 
 

TrueTears:

--- Quote from: QuantumJG on March 02, 2010, 03:01:19 pm ---
--- Quote from: TrueTears on March 01, 2010, 09:43:07 pm ---if f has a power series expansion: then the maclaruin series is just a special case of it: namely, centered at 0. (a = 0)

but that's not the slick part, the coolest part is the relationship between the coefficients of the power series f(x) and the derivatives of f(x), thats the part i love the most!!

--- End quote ---

So what this is impliying that if,





So

  becomes 
 

--- End quote ---
don't you mean when f(x) is centered around 0? not f(a=0)?

it's not implying anything... just that the expansion is "centered" around 0 so that the power series expansion provides a good approximation around 0 xD

QuantumJG:
Prove that:



What would be a good way to do this proof?

TrueTears:


Right angle triangle, opposite is , hypotenuse is

Thus tan of this angle is .

Thus

QuantumJG:
What is the difference between and ?

Also when you are asked:

write sin(x) as an element of is that just:

sin(x) =

Also what is: & ?

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