Evaluate the following polynomial at x = 3.17 y = x^3 - 5x^2 + 4x - 0.15 (b) Rep

Question

Evaluate the following polynomial at x = 3.17 y = x^3 - 5x^2 + 4x - 0.15 (b) Repeat (a) using 3-digit arithmetic with rounding after each mathematical operation. Consider raising to a power to be one operation. Evaluate the true percent relative error. Refer to the text for the definition of true percent relative error. (c) An alternate expression of the polynomial is shown below. Evaluate this alternate expression using 3-digit arithmetic with rounding after each mathematical operation. Evaluate the true percent relative error and compare the result with part (b). y = ((x-5)x + 4)x-0.15

Explanation / Answer

a.
y = x3 - 5x2 + 4x - 0.15
   = (3.17)3 - 5(3.17)2 + 4(3.17) - 0.15
   = 31.855013 - 5(10.0489) + 12.68 - 0.15
   = 31.855013 - 50.2445 + 12.68 - 0.15
   = -5.859487

b.
y = x3 - 5x2 + 4x - 0.15
   = (3.17)3 - 5(3.17)2 + 4(3.17) - 0.15
   = 10.0 * (3.17) - 5 *(10.0) + 12.7 - 0.15
   = 31.7 - 50 + 12.7 - 0.15
   = -18.3 + 12.7 - 0.15
   = -5.6 - 0.15
   = -5.75

Percentage Relative Error = AbsoluteError/TrueValue x 100
                                             = 0.109487 / -5.859487 * 100
                                             = -1.869

c
y = ((x - 5) x + 4) x - 0.15
   = ((3.17 - 5) 3.17 + 4) 3.17 - 0.15
   = (-1.83 * 3.17 + 4) 3.17 - 0.15
   = (-5.80 + 4)3.17 - 0.15
   = -1.8 * 3.17 - 0.15
   = -5.71 - 0.15
   = -5.86

Percentage Relative Error = AbsoluteError/TrueValue x 100
                                             = 0.000513 / -5.859487 * 100
                                             = -8.76e-2

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