Question

Use zeroth- through fourth-order Taylor series expansions to predict f(5) for 𝑓(𝑥) = 25𝑥^4 − 6𝑥^3 + 7𝑥^2 − 88𝑥 Use a base point at x = 1, and compute the true percentage error for each approximation. (Round the final estimated values to the nearest whole numbers and the error values to two decimal places.) Enter the desired values in the spaces provided in Canvas. Problem 7 (20 points) Write a MATLAB program or Excel macro that will solve for sin(x) using the infinite series below. The program should have 2 inputs: the value of x and the stopping criterion (i.e. maximum desired true fractional error). Loop and add terms until the true fractional error is less than the stopping criterion. Report the approximate value of sin(x) and the number of terms needed. 𝑠𝑖𝑛(𝑥) = 𝑥 − 𝑥^3/3! + 𝑥^5/5! − ... = 𝑛 = 0 to ∞ ∑ (−1)^𝑛𝑥^(2𝑛+1)/(2𝑛+1)! Order Value Error ε|% 0 ? ? 1 ? ? 2 ? 84.98 3 ? ? 4 14610 ?

          Use zeroth- through fourth-order Taylor series expansions to predict f(5) for
𝑓(𝑥) = 25𝑥^4 − 6𝑥^3 + 7𝑥^2 − 88𝑥
Use a base point at x = 1, and compute the true percentage error for each
approximation. (Round the final estimated values to the nearest whole numbers and the
error values to two decimal places.) Enter the desired values in the spaces provided in
Canvas.
Problem 7 (20 points)
Write a MATLAB program or Excel macro that will solve for sin(x) using the infinite
series below. The program should have 2 inputs: the value of x and the stopping
criterion (i.e. maximum desired true fractional error). Loop and add terms until the true
fractional error is less than the stopping criterion. Report the approximate value of sin(x)
and the number of terms needed.
𝑠𝑖𝑛(𝑥) = 𝑥 − 𝑥^3/3! + 𝑥^5/5! − ... = 𝑛 = 0 to ∞ 
∑ (−1)^𝑛𝑥^(2𝑛+1)/(2𝑛+1)!
Order Value Error ε|%
0 ? ?
1 ? ?
2 ? 84.98
3 ? ?
4 14610 ?

Added by Jesse E.

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