# Help Finding Explicit Formula and Error Bound

• October 30th 2010, 07:36 AM
Porter1
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• October 30th 2010, 08:20 AM
Ackbeet
Sounds like the Taylor polynomial with remainder, to me.
• October 30th 2010, 08:27 AM
bandedkrait
I can't think of a formal approach to this problem, but the $p(x)$ is nothing but the Lagrange polynomial interpolation for a set of n+1 data points, while the second $P(x)$ is the Taylor's series approximation of $f(x)$ about $x=x0$

Look up the definition of a nth order Taylor's polynomial approximation about a point x=xo and you will have both questions answered.

But it would be more useful if someone could throw light on the derivation of the Taylor series expansion.

1)http://en.wikipedia.org/wiki/Lagrange_polynomial
2)http://en.wikipedia.org/wiki/Taylor_series