Q5) Fill the Newton's Divided Differences Table, then answer the following: 20 Deg. 2nd 3 (x) 2.718 1st FlXo. Xal 7.389 20,086 3. 4. F[x0]= IL. F[x0,x1]= III. F[x0,x1x2]= IV. F(x0,x1,x2,x3]= V. F(2.5)-7 54.598 1.
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- Calculate f (3.5) with newton's interpolation of order 1, choose the order of data used to produce good accuracyUse the data below to estimate the value of f(6) to two (2) decimal digits using Backward Newton-Gauss Interpolation Formula.How does Taylor’s formula for a function ƒ(x, y) generate polyno-mial approximations and error estimates?
- Use Newton's meathod given f(x) = x3 + 3x + 1, if x1 = -(1/3) as the first approximation to find x3 to four decimal placesApply Newton’s Method to f and initial guess x0 to calculate x1, x2, x3: f (x) = x3 + x + 1, x0 = −1What happens in Newton’s Method if your initial guess happens to be a local min or max of f ?