If f(1) = 1 and f(n) = f(n - 1) - 5 then find the value of f(5) .

Question 3 (a) consider the data. 00 0 25 0.5 05 () construct the divaded difference's table for the data (u) construct the newton form of the polynomial of lowest degree that interpolates /() at these points (3) (ii) suppose that these data were generated by the function cos 2 ()=1+ 2 use the next term rule to approximate the error ip(z)- f() over the interval 0,0 5 your answer should be a pumber 3 (b) let f ((z) co+ clco, ci e r) set up the normal equations to find the least squares best fe f to approximate the data x y 2 y2 (c) find the constants a,b and c such that stz)(z-1+b(z-1)2+6(z-1)+1 cr +182-30+19- 1sz< 2 25z< 3 (9) s a natural cubic splhne [25] |turn over