Solve the given information Let f(x) = sin x. Determine an error bound for the approxiamtion f(0.34) = sin 0.34. and compare it to the actual error.

sodni3 2020-12-03 Answered
Solve the given information Let f(x)=sinx. Determine an error bound for the approxiamtion f(0.34)=sin0.34. and compare it to the actual error.
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Jozlyn
Answered 2020-12-04 Author has 85 answers

We to find an error bound for the approximation and compare it to the actual error. The exact value of sin(0.34)=0.33348709214081. So, the actual error is (0.333487092140810.33349)=2.91×106 The bound for the error on [0.30, 0.35] is given by, |f(x)H5(x)|=|f6(ξ)6!(x=0.30)2(x0.32)2(x0.35)2|=|sin(ξ)720(x0.30)2(x0.32)2(x0.35)2| When ξ[0.30,0.35]. Evaluating this error term at x = 0.34 yields,

|sin(0.34)H5(0.34)|=|sin(ξ)720(0.04)2(0.02)2(0.01)2|
|sin(0.35)720(0.04)2(0.02)2(0.01)2|
 3.05×1014

This bound is not inconsistent with the actual error, because the approximation was computed using five-digit rounding arithmetic.

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Jeffrey Jordon
Answered 2021-12-16 Author has 2313 answers

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