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12 Nov 2019
Using calculator, we can find the value of function f(r) at (x = 1 & x-1.2) e1.1x1 = 3.004166023946433 and el.1Ã1.2ã¼3.743421377260863 Let's pretend that we don't know the exact answer at x = 1.2, but we know the exact answer at 1. f(x) = el.lz at zo,-l is f(x) = e1.1ã¼3.0042 f(x) = el.lz at ë = 1.2 is f(x)-e1.32 =? Derive Taylor for function f(x)-el.lz near z = 1. Use the value off (1-e1.1-3.0042 to determine the value of this function at x = 1.2 in the following cases: (a) Use only the first term of Taylor series (b) Use two terms of Taylor series c) Use three terms of Taylor series (d) Use four terms of Taylor series For each case, calculate the true error, true relative error, approximate error and approximate relative error. Make a table for the final results. Taylor Series: 2! 3! True relative error: TrueValue-EstimatedValuel Et-relative TrueValuel Use the following definition for approximate relative error: NewEstimatedValue - OldEstimatedValuel NewEstimatedValue Ea-relative Notes: 4 ~ 6 digits in each number should be well enough
Using calculator, we can find the value of function f(r) at (x = 1 & x-1.2) e1.1x1 = 3.004166023946433 and el.1Ã1.2ã¼3.743421377260863 Let's pretend that we don't know the exact answer at x = 1.2, but we know the exact answer at 1. f(x) = el.lz at zo,-l is f(x) = e1.1ã¼3.0042 f(x) = el.lz at ë = 1.2 is f(x)-e1.32 =? Derive Taylor for function f(x)-el.lz near z = 1. Use the value off (1-e1.1-3.0042 to determine the value of this function at x = 1.2 in the following cases: (a) Use only the first term of Taylor series (b) Use two terms of Taylor series c) Use three terms of Taylor series (d) Use four terms of Taylor series For each case, calculate the true error, true relative error, approximate error and approximate relative error. Make a table for the final results. Taylor Series: 2! 3! True relative error: TrueValue-EstimatedValuel Et-relative TrueValuel Use the following definition for approximate relative error: NewEstimatedValue - OldEstimatedValuel NewEstimatedValue Ea-relative Notes: 4 ~ 6 digits in each number should be well enough
Patrina SchowalterLv2
7 Mar 2019