(a) Show directly for unifornn spacing h-xi-zo-x2-xi that A fo and 2h2' (b) Establish Newton's forward-differen...
4. (a) Show directly for uniform spacingh =r1-ro=r2-1 that 42 fo f\ro, I1, F2] = 2h? Afo f{rO, x1] h and where fi f(r), Afi = fi+1-fi, and A?f,= Afi+1=Afi (b) Establish Newton's forward-difference form of the interpolating polyno mial with uniform spacing P2(r) =fo+ where p2 is the polynomial of degree < 2 that interpolatesf at ro, , , and =o+sh. Here, ()--1)m+1) is a binomial coefficient.
8396 5101281 5 8 2 0 1 12 ( 4 2 1 ) ) ) 0000 f-000 0246802 (i) Defining fo-f(zo). Л that the quadratic f(x) and f2 f(x2), where Zo-x1-h and x2-xuth, show 2 , f2 - jo 2h2 2h is the quadratic interpolating function for fo, fı and f2 (i.e. show that p(x)-f) 4] (ii) Use the interpolating polynomial p(x) as defined above, with Zo-12, xỉ-1.4 and 22 -1.6 (and fo, fı and f2 given by the table...