Find the relative error of approximation of f\'(0.6) by the Left End 5-point for

Question

Find the relative error of approximation of f'(0.6) by the Left End 5-point formula with mesh size h - 0.010, where f(x) - arctan(3x). (A) 9.7092 middot 10^-7 (B) 1.1415 middot 10^-7 (C) 4.0631 middot 10^-9 (D) 2.4682 middot 10^-7 (E) 4.5072 middot 10^-7 (b) Find the relative error of approximation of f'(1.0) by the Left End 5-point formula with mesh size h - 0.005, where f(x) - arctan(8x). (A) 7.6668 middot 10^-8 (B) 1.7629 middot 10^-9 (C) 1.4804 middot 10^-7 (D) 4.1890 middot 10^-7 (E) 1.3021 middot 10^-8

Explanation / Answer

If we choose X0iXi0 to be left end point Xi-1 xi-1 of interval [xi-1,xi][xi-1,xi] then this is call left point end approximation,

If we choose x0i Xi0 to be right end point xixi of interval [xi-1,xi][xi-1,xi] then this approximation is called right end point approximation.

If we choose x0i xi0 to be midpoint of interval [xi-1,xi][xi-1,xi] then this approximation is called mid point rule approximation.

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