Given the function y(x) = sin(4+ sin(2x)) and the mesh x₁ = xo + ik, where co ㅠ 2' ㅠ determine the central finite difference for the first derivative of y with step size k = 14 (c) Enter the absolute error at mesh point i = 4. At the same point, also calculate the exact first derivative y'(x). Calculate the absolute value of the error of the finite difference approximation at the point x₁. Work to at least 6 decimal places throughout and enter your answers to 2 decimal places. (a) Enter the finite difference approximation (b) Enter the exact derivative

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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Section2.1: Tables And Trends
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Given the function
y(x): = sin(4 + sin(2x))
and the mesh x₁ = xo + ik, where co
determine the central finite difference for the first derivative of y with step size k
-
ㅠ
2
(c) Enter the absolute error
ㅠ
14
At the same point, also calculate the exact first derivative y'(xi).
Calculate the absolute value of the error of the finite difference approximation at the point ï¿.
Work to at least 6 decimal places throughout and enter your answers to 2 decimal places.
(a) Enter the finite difference approximation
(b) Enter the exact derivative
Select
at mesh point į = 4.
(d) If we were to divide the step size by 10, the error will be approximately multiplied by a factor of
Transcribed Image Text:Given the function y(x): = sin(4 + sin(2x)) and the mesh x₁ = xo + ik, where co determine the central finite difference for the first derivative of y with step size k - ㅠ 2 (c) Enter the absolute error ㅠ 14 At the same point, also calculate the exact first derivative y'(xi). Calculate the absolute value of the error of the finite difference approximation at the point ï¿. Work to at least 6 decimal places throughout and enter your answers to 2 decimal places. (a) Enter the finite difference approximation (b) Enter the exact derivative Select at mesh point į = 4. (d) If we were to divide the step size by 10, the error will be approximately multiplied by a factor of
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