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Given the function y(x) = sin(4+ sin(2x)) and the mesh x = xo + ik, where co π 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'(x₂). 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 (d) If we were to divide the step size by 10, the error will be approximately multiplied by a factor of

Given the function y(x) = sin(4+ sin(2x)) and the mesh x = xo + ik, where co π 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'(x₂). 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 (d) If we were to divide the step size by 10, the error will be approximately multiplied by a factor of

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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y(x)=sin(4+sin(2x)) x₁ = xo + ik 1=4 14 Note: According to the guidelines we are allowed to solve 3 subparts at a time. Please post rest of the subparts separately. Step 2: Finding the first derivative using central difference f(x+k)-f(x-k) where is the step length. 2k f'(x)= X4=X+4k -147+8 28 бл 28 3 T 14 4 T 14 :. f'(x)= f(x+k)-f(x-k) 2k 1 ( - ² + 7) - (- = - 74 ) 14 = f(-37) = (-7)-(-²7) 푸 sin (4+ sin(-27))-sin(4+ sin(-4)) 푸 -0.076501-0.116257 # -0.43 Step 3: Finding the exact value y(x)=sin(4+sin(2x)) y'(x)=2cos(4+sin(2x))cos(2x) y'(-34) = = -0.442024 Step 4: Finding the absolute error EA=True value-Appoximate value =1-0.44+0.431 = 0.01 Solution Hence (a) Enter the finite difference approximation -0.43 (b) Enter the exact derivative -0.44 (c) Enter the absolute error [0.01
Transcribed Image Text:y(x)=sin(4+sin(2x)) x₁ = xo + ik 1=4 14 Note: According to the guidelines we are allowed to solve 3 subparts at a time. Please post rest of the subparts separately. Step 2: Finding the first derivative using central difference f(x+k)-f(x-k) where is the step length. 2k f'(x)= X4=X+4k -147+8 28 бл 28 3 T 14 4 T 14 :. f'(x)= f(x+k)-f(x-k) 2k 1 ( - ² + 7) - (- = - 74 ) 14 = f(-37) = (-7)-(-²7) 푸 sin (4+ sin(-27))-sin(4+ sin(-4)) 푸 -0.076501-0.116257 # -0.43 Step 3: Finding the exact value y(x)=sin(4+sin(2x)) y'(x)=2cos(4+sin(2x))cos(2x) y'(-34) = = -0.442024 Step 4: Finding the absolute error EA=True value-Appoximate value =1-0.44+0.431 = 0.01 Solution Hence (a) Enter the finite difference approximation -0.43 (b) Enter the exact derivative -0.44 (c) Enter the absolute error [0.01
Given the function y(x): = sin(4 + sin(2x)) and the mesh x�� = 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 x�� = 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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