Solve all Numerical analysis problems rigorously:

`f(x)=X, Xo = 1/2x4 find the theoretical error bound on x4 fix)=ex, Xo = 0 find Pn(x), Rn(x), and the general term. find the bound on the other term max 14x24 | Rn (x) | = | [ 0 (1-j) | } (x) ) /2 - () (n+1) Show the cost of the algorithm. P= POsign@power factorial nti Write the psuedocode for f(x) = cosx, Xo = O Pn (x) = 2/1/2 (-1)x0 (2i)! C=0 -(x-xo) is 0(n) powerx = powerxxx factorial = factorial (2i+1)/2i+2)