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# Consider the case where we have a mixed set of values (I, y) where y : f(I) but still would like to nd nite difference formulas. Consider for this...

For the following problem, parts a and c need to be solved "on paper", while part b requires a code in Python.

Consider the case where we have a mixed set of values (I, y) where y : f(I) but still would like to ﬁnd ﬁnite difference formulas. Consider for this question thecase where we know the values ofﬂx) atxo : 0.x. : Ax,x2 : 2M, and the value ofy' :f’(x) at x0 = 0 only. [a] (1'0) Find a ﬁnite difference approximation fOI the second derivative of the formfun-J) _ 2:0 Win-ti} + bin-’2]IM2 ﬁx that is as accurate as possible in the asymptotic limit Ax —> 0. Type Markdown and LaTeX: 0:2 [b] (10) Test the ﬁnite difference formula from part (a) on icosmrand 2.x“ plotting the order of convergence for each. a? INSERT CODE THEREraise NotImplementedErrorl:"Replace this statement with your: solution.“ to] (5) Explain your results from part (a) and (b) given what you know of the functions and the ﬁnite difference approximation you derived. Type Markdown and LaTeX: «12