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

The absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value. The percentage error is the relative error expressed in terms of per 100.

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