Given a function F(x), F' continuous, we have from the mean-value theorem that in evaluating F...

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Given a function F(x), F' continuous, we have from the mean-value theorem that in evaluating F at x the relative error from this source alone is F(x) - F(x) F(x + ex) - F(x) F'()[(x + εx) - x] F(x) F(x) F(x) = EX i. F(x) = xk, for various values of k and x; ii. F(x) = e, for large values of x; iii. F(x)= sin(x), for small values of x; iv. F(x) = x² - 1, for x near 1; v. F(x) = cos(x), for x near 7/2. F'(x) F(x) Analogously, F(x) – F(x) F(x) = exF'(x). Use these formulas to give estimates of absolute and relative error if Given a function F(x), F' continuous, we have from the mean-value theorem that in evaluating F at x the relative error from this source alone is F(x) - F(x) F(x + ex) - F(x) F'()[(x + εx) - x] F(x) F(x) F(x) = EX i. F(x) = xk, for various values of k and x; ii. F(x) = e, for large values of x; iii. F(x)= sin(x), for small values of x; iv. F(x) = x² - 1, for x near 1; v. F(x) = cos(x), for x near 7/2. F'(x) F(x) Analogously, F(x) – F(x) F(x) = exF'(x). Use these formulas to give estimates of absolute and relative error if

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