(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have the following question to answer:

Show that

(X^2/h^2)*((1/2*y1) - y2 + (1/2*y3)) + (X/h)*((-1/2 y1)+(1/2 y3))+y2 (sorry about the format)

is equal to (taylor expansion):

y = y2+(x(dy/dx)¦0 + (x^2/2*((d^2)y)/(dx^2))¦0

2. Relevant equations

also given in dy/dx¦0 is value of dy/dx when x = 0

and

dy/dx¦0 (approximately) = 1/2h (y(+h)-y(-h))

3. The attempt at a solution

I know how to derive the quadratic, but I never really got the hang of taylor expansions so I'm lost.

I can see that there is a double derivative term, but as this i the derivative of the dy/dx¦0 term with no x values in it, does it then become zero? Also, all I have ended up with for the taylor expansion is:

y= y2 + x(1/2h(y(+h)-y(-h))) + x^2/2 ((double derivative term = 0)

giving

y= y2 + x(1/2h(y(+h)-y(-h))) and then I've tried to multiply out the brackets.

I can see that I've gone wrong as I can't get an answer.

Can anyone point me in the right direction please??

Cheers

Kel

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# Need help proving that a quadratic interpolation formula is same as taylor expansion

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