Q4. Use Newton forward-difference formula and construct appropriate interpolating polynomial and approximate f(0.5) Xi -1 0 1 2 fi 1 -1 1 13

P=S/(S+F) Express S in terms of F and P

Q1/ From the following set of data: A) Calculate f(0.25), using Newton's divided difference formula B) Calculate f (0.25), using Newton-Gauss interpolation method C) Calculate the slope of the polynomial equation at f (0.25) X 0.20 0.22 0.24 0.26 0.28 0.30 0.32 f x) 1.6596 1.6698 1.6804 1.6941 1.7028 1.7146 1.7268

I need the answer as soon as possible

Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5. Usethetableweusedinclasstofindthe coefficients.

Solve clearly, hand written.

Use the Newton forward difference formula to construct interpolating polynomials of degree three for the following data. Approximate f(-0.3) f(-0.75) = -0.0718, f(-0.5) = -0.0247, f(-0.25) = 0.3349, f(0) = 1.1010

Find the interpolating polynomial of the following point and function using Newton's interpolation process. y = ln ( x + 2 ) at x = [-1,2]. Find the interpolating polynomial of the following function using Direct Fit Polynomials. y = exp( 2-x ) at x = [-1,2].

a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. 1 f(x) = 1 --, a = 1; approximate 1.08

Is (f og)(0) = (fg)(0)? Justify answer