Easy limit

ahh any function can be written as the a taylor series. whats the Taylor's theorem good for?

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Originally posted by bugzpodder
ahh any function can be written as the a taylor series. whats the Taylor's theorem good for?

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what's taylor's theorem?:confused:

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Originally posted by bugzpodder
ahh any function can be written as the a taylor series.

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Originally posted by MrPolite
what's taylor's theorem?:confused:

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Taylor's Theorem states:
Suppose that f has n+1 continous derivatives on an open interval
I containing 0. Then, for each x E I,
f(x) = f(0) + f'(0)x + (f''(0)x²)/2! + ... + (f⁽ⁿ⁾(0)xⁿ)/n! + R_n+1(x),
where the remainder R_n+1 is given by the formula
R_n+1(x) = 1/n! * integral(a=0 b=x)f⁽ⁿ⁺¹⁾(t)(x-t)ⁿdt

what is it used for?

Hi Bugz. AFAIK:

a) I think in calculators/computers for calculating functions like e^x
b) Integrating functions that cannot normally be integrated
c) Generally making approximations