00:01
Hi, for part a of the question we can use the leckranges interpolation formula to compute f of 3 from the given experimental data.
00:07
So, this is the formula here x1, xn are the known data points and y0, y1 up to yn are the corresponding function values.
00:14
Substituting the given data into the formula, so we get f of 3 is equal to minus 2 of 3 minus 4 plus minus 1 of 3 minus 0, 3 minus 2 and 3 minus 4 by 1 minus 0 and 1 minus 2 and 1 minus 4.
00:45
So plus 6 into 3 minus 0 and 3 minus 1, 3 minus 4 by 2 minus 0 and 2 minus 1, 2 minus 4.
01:00
So, into plus 62 of again we write 3 minus 0, 3 minus 1 and 3 minus 2 by 4 minus 0, 4 minus 1, 4 minus 2.
01:17
So which is equal to we get the answer that is 11.
01:21
F of 3 is equal to 11.
01:26
And for part b of the question we are given differential rule of the formula.
01:29
We need to find the values of alpha 0, alpha 1, alpha 2.
01:32
So the rule is exact.
01:34
When f of x is a polynomial of degree s is equal to 0.
01:36
To do this we can use the taylor series of expansion of f of x around x0...