Let Xo = 0, X,= ob and X2 = 0.9 Construct interpolation polgnonial at degree at...

Question

Question

Let Xo = 0, X,= ob and X2 = 0.9 Construct interpolation polgnonial at degree at most two to approximate f(0.45) and find the

Answer 1

Answer #1

Here the values of x are not equidistant... So we use Lagrange's interpolation formula to find f(x) and then find f(0.45)

Find the attachment for solution and absolute error is 0.0032

х f(x) 0 0 0.6 0.47 0.9 0.6418 X = 0.45 Solution: The value of table for x and y x 0 | 0.6 0.9 y O 0.47 0.6418 Langranges In

A for f(x) = ln(x+1) put xz 0.45 f(0.45) = ln (1:45) = 0.77 16 T from interpolated value f60/45) = 0.3683 → t Absolute Error

Here absolute error is 0.0032

Answer 2

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