Question

The second divide difference of x^2 is?​ please help..​

Answer 1

Answer:

Newton’s divided difference interpolation formula is a interpolation technique used when the interval difference is not same for all sequence of values.

Suppose f(x0), f(x1), f(x2)………f(xn) be the (n+1) values of the function y=f(x) corresponding to the arguments x=x0, x1, x2…xn, where interval differences are not same

Then the first divided difference is given by

f[x_0, x_1]=\frac{f(x_1)-f(x_0)}{x_1-x_0}

The second divided difference is given by

f[x_0, x_1, x_2]=\frac{f[x_1, x_2]-f[x_0, x_1]}{x_2-x_0}

and so on…

Divided differences are symmetric with respect to the arguments i.e independent of the order of arguments.

so,

f[x0, x1]=f[x1, x0]

f[x0, x1, x2]=f[x2, x1, x0]=f[x1, x2, x0]

By using first divided difference, second divided difference as so on .A table is formed which is called the divided

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Answer 2

Step-by-step explanation:

find the second divided difference of x²