In this problem, you will derive an approximation for f(x)dx and an error bound for the...

 

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In this problem, you will derive an approximation for f(x)dx and an error bound for the method a. If the interval is broken up into 2 equal length subintervals, how long is each subinterval? b. Find the midpoint (x value) of each of these 2 subintervals. Call them X, and.x₂ c. Find , and c₂ such that [ƒ(x)dx=qf(x₂)+c₂f (x₂) has the greatest possible degree of precision. d. Find the degree of precision. e. Compute the error (exactly) in using the method to compute is the lowest whole number power such that the method is not exact. f. Assume the error bound has the form max c₂h f)(x) where q and r are whole numbers and this error is exact for the case in part e. Find q.r' and c 27 12₁x² -2h xdx where p In this problem, you will derive an approximation for f(x)dx and an error bound for the method a. If the interval is broken up into 2 equal length subintervals, how long is each subinterval? b. Find the midpoint (x value) of each of these 2 subintervals. Call them X, and.x₂ c. Find , and c₂ such that [ƒ(x)dx=qf(x₂)+c₂f (x₂) has the greatest possible degree of precision. d. Find the degree of precision. e. Compute the error (exactly) in using the method to compute is the lowest whole number power such that the method is not exact. f. Assume the error bound has the form max c₂h f)(x) where q and r are whole numbers and this error is exact for the case in part e. Find q.r' and c 27 12₁x² -2h xdx where p