Tema4 - 4.18 f(x) = x-1-1/2*sin(x) f '(x) = 1-1/2*cos(x) f...

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Unformatted text preview: 4.18 f(x) = x-1-1/2*sin(x) f '(x) = 1-1/2*cos(x) f ''(x) = 1/2*sin(x) f '''(x) = 1/2*cos(x) f IV (x) = -1/2*sin(x) Using the Taylor Series Expansion (Equation 4.5 in the book), we obtain the following 1 st , 2 nd , 3 rd , and 4 th Order Taylor Series functions shown below in the Matlab program-f1, f2, f4. Note the 2 nd and 3 rd Order Taylor Series functions are the same. From the plots below, we see that the answer is the 4 th Order Taylor Series expansion . x=0:0.001:3.2; f=x-1-0.5*sin(x) ; subplot(2,2,1); plot(x,f);grid;title( 'f(x)=x-1-0.5*sin(x)' );hold on f1=x-1.5 ; e1=abs(f-f1); %Calculates the absolute value of the difference/error subplot(2,2,2); plot(x,e1);grid;title( '1st Order Taylor Series Error' ); f2=x-1.5+0.25.*((x-0.5*pi).^2); e2=abs(f-f2); subplot(2,2,3); plot(x,e2);grid;title( '2nd/3rd Order Taylor Series Error' ); f4=x-1.5+0.25.*((x-0.5*pi).^2)-(1/48)*((x-0.5*pi).^4); e4=abs(f4-f); subplot(2,2,4); plot(x,e4);grid;title( '4th Order Taylor Series Error' );hold off 1 2...
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This note was uploaded on 03/13/2012 for the course AEROSPACE 301 taught by Professor Pfchang during the Spring '12 term at Shandong University.

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Tema4 - 4.18 f(x) = x-1-1/2*sin(x) f '(x) = 1-1/2*cos(x) f...

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