Question

4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro) is given by f(zo + h) + cf (zo + 21) + 0(h2). f' (zo) = af(xo) + What is the precise form of the error term? Using the formula approximate f' (1) where r) = e* for h 1/(2p) for p = 1 : 15, Form a table with columns giving h, the approximation, absolute error and absolute error divided by 2. For each indicate to which values they are converging. Finally, verify that the last column appears to be converging to a value derived using the error term.

Answer 1

Taylor serues 足! all fill ca) x (x-a) 3 I Civin form Eor tomula h+l nf

1 3 for thi-, derivative - .texL-İLL _ have K 0,l, 2,3 tor error nキリ! czx So le have baund a

here Pn(1) is closes to pow(10,-5)

)2. 1182 78 So 3.66x10 e-80 ti ) =