Question

oth), wo - ) Problem 1. In this problem, we use to the to--) to approximate f'(o), i.e. f'(30) (Hint: Use the Taylor expansions for both f(+ h) and f(xo-h)). (A). Show, using the Taylor expansions for both f(10+h) and f(10-h), that the leading term of the error is "( 70) |h2.

Answer 1

Using Taylor's Series Expansion. We know that ++++h) = 4(4) + h 4'60) + Sum) + n° {"cx.) + bil ps3 *** 4670-) = 467.) - h f'(x) +h? f'(X.) - h} {"(0) + " **** 3! ... ☺ Now, Subtracting from 6, we have +(Xo+h)- 4(o-h) - ah f'(7.) + RA? {"(40) +24," ** = zh[ t'or) + "%) * () +- – 2 " ) + t'(xo) th f (xo). = f(xoth) - f(xoth) 2h

f(xoth) - f(xo-h) - (x) + f (x0) + ... 2h 5! So, Error to approximate f'(xo) by finite difference is of orden i f(xoth)-f(xo-h) 2h b f"(x)]. I and leading team of essor is

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