multiple choice

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- May 21st 2007, 11:53 AMharryTaylor's theorem
multiple choice

- May 22nd 2007, 01:44 PMCaptainBlack
(1) Find the sum:

Consider this as a function of (note the negative sign in front of the term in

I presume is a mistake), the derivative of this is:

which is a geometric series and it converges for .

So write down the sum of this last series, then integrate with the constant

of integration set so that the integral is zero for , and that

is your answer (it looks like (d) to me but you will need to check).

RonL - May 22nd 2007, 02:28 PMThePerfectHacker
There are many verions, I use the the following one.

**Taylor's Theorem (Lagrange):**Let be differenciable on (with ) and for the remainder is given by for some between and . Where the remainder is the difference between the function and its degree Taylor polynomial , defined as and .

So, if then on

Then,

So it is 2 decimal points.