. Assume a continuous function f(x) defined on x axis with a uniform grid spacing of...

. Assume a continuous function f(x) defined on x axis with a uniform grid spacing of h. The first and second derivatives of function can be approximated using information at more grid points giving rise to higher-order approximations. Using appropriate Taylor series expansions about location x, find the leading order truncation terms for the following approximations. Also indicate the order of accuracy for each approximation. Show all steps and box the final answers. Note: Look for the location at which a particular formula is written. For example, the first one below is at the location x. All your Taylor series expansions should be around x in this case. If a formula is approximating at x + h, all your Taylor series expansions should be around x + h (e.g. for part 4).

f(x + h) ≈ 2f(x) − f(x − h)

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Ally Wells answered 1 year ago

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