Given the following function: f(x)=1.01e^{4x}-4.62e^{3x}-3.11e^{2x}+12.2e^{x} - 1.99 a)Use three-digit rounding frithmetic, the assumption that e^{1.5

Suman Cole 2020-11-01 Answered
Given the following function: f(x)=1.01e4x4.62e3x3.11e2x+12.2ex1.99 a)Use three-digit rounding frithmetic, the assumption that e1.53=4.62, and the fact that enx=(ex)n to evaluate f(1.53) b)Redo the same calculation by first rewriting the equation using the polynomial factoring technique c)Calculate the percentage relative errors in both part a) and b) to the true result f(1.53)=7.60787
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svartmaleJ
Answered 2020-11-02 Author has 92 answers

a) f(x)=1.01e4x4.62e3x3.11e2x+12.2ex1.99

f(x)=1.01(ex)44.62(ex)33.11(ex)212.2ex1.99(as enx=(ex)n)

f(1.53)=1.01(e1.53)44.62(e1.53)33.11(e1.53)2+12.2e1.531.99

=1.01(4.62)44.62(4.62)33.11(4.62)2+12.2(4.62)1.99(as e1.53=4.62)

=1.01(455.583)4.62(98.611)3.11(21.344)+56.3641.99

=460.139455.58366.380+54.374

=7.45

Therefore, the value of f(1.53) abtained by this method is -7.45.

b) The given function can be factorized sa follows. f(x)=1.01(ex+1.715)(ex0.173)(ex1.415)(ex4.702) On substituting x=1.53 and using e1.53=4.62, we get f(1.53)=1.01(4.62+1.715)(4.620.173)(4.621.415)(4.624.702)

=1.01(6.335)(4.447)(3.205)(0.082)

=7.478

Therefore, the value of f(1.53) obtained by this method is -7.478.

c) Percentage error δ is given by δ=|νAνEνE|100% Here νA is the actual value and νE is the expected value which is -7.60787 in this case. For the value obtained in part (a), the percentage error is δa=|7.45+7.607877.60787|100%

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Jeffrey Jordon
Answered 2022-01-23 Author has 2495 answers

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