Answer to Question #229352 in Electrical Engineering for Alock kumar

Question #229352

For the following voltage function, find the numerical differentiation of first order using the finite divided-difference formula at a point, 1, - 4.5 s with step forward, backward and center finite divide-difference formula at a point t1=4.5 s with step size, h=0.i s, where i=72


v(t) = 20sint-t^3/18


Evaluate the values using the conventional differentiation formula aiso and hence comment which numerical method produce better result based on the percentage of true error.


1
Expert's answer
2021-08-27T02:35:42-0400

"\\frac{d}{dt}\\left(20\\sin \\left(t\\right)-\\frac{t^3}{18}\\right)\\\\\n\\mathrm{Apply\\:the\\:Sum\/Difference\\:Rule}:\\quad \\left(f\\pm g\\right)'=f\\:'\\pm g'\\\\\n=\\frac{d}{dt}\\left(20\\sin \\left(t\\right)\\right)-\\frac{d}{dt}\\left(\\frac{t^3}{18}\\right)\\\\\n=20\\cos \\left(t\\right)\\\\\n=20\\cos \\left(t\\right)-\\frac{t^2}{6}"


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