Problem 2: 45 points Use zero- through second-order Taylor series expansions to

Question

Problem 2: 45 points Use zero- through second-order Taylor series expansions to predict f3) for the true percent relative error (15 points) Use forward difference approximations of oth) to estimate the first derivative at x - 2 using a step size of h- 0.2. Estimate the true percent relative error (15 points) The Stefan-Boltzmann law can be employed to estimate the rate of radiation of a. fe=contrat. Compute Stefan-Boltzmann law can be employed to estimate the rate of radiation of energy H from a surface, as in: error (ls pointse the first derivative at c. Where H is in watts A the surface area (m'), e the emissivity that characteri - the surface area (m', e the emissivity that characterizes the emitting properties of Where H is in watts A the surface (dimensionless), = a universal constant Stefan-Boltzmann (5.67x108 Wmhe) , and T-absolute

Explanation / Answer

f(x) = 5x4 + 2x-2 + 1/x - 20

f '(x) = 20x3 - 4x-3 - x-2

f ''(x) = 60x2 + 12x-4 + 2x-3

f(3) = 385.55

f '(3) = 539.74

f ''(3) =540.22

f(x) = f(3) + f '(3) (x - 3) + f ''(3) (x - 3)2 /2! = 385.55 + 539.74 (x - 3) + 270.11(x - 3)2

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