Complete using Matlab

4. Use the first derivative functions to estimate the dy/dx value for y=sin(x) at x=pi/3. Use a step size (delta x) of pi/10. Compute the magnitude of the error for each approximation (backward, forward, centered).

Use functions provided (can be copied and pasted into matlab)

(forward and Backward apporximation)

function [ firstderivative ] = firstdfrontback( x,y ) % this function finds the first derivative using the forward and backward % method and saves a matrix with three columns, the firsst being th x % values, the second containing the forward apporximation, and the third % containing the bacwards apporximation orig_length=length(x); firstderivative = zeros(length(y),3); if(length(x)> length(y)) orig_length = length(y); firstderivative = zeros(length(x),3); end for i=1:orig_length-1 h=x(i+1)-x(i); firstderivative(i,1)=x(i); firstderivative(i,2)=(y(i+1)-y(i))/h; end for i=orig_length:length(x) firstderivative(i,1)=x(i); firstderivative(i,2)=NaN; end for i=orig_length+1:length(y) firstderivative(i,1)=NaN; firstderivative(i,2)=NaN; end firstderivative(1,3)=NaN; for i=2:orig_length h=x(i)-x(i-1); firstderivative(i,3)=(y(i)-y(i-1))/h;

end for i=orig_length+1:length(x) firstderivative(i,1)=x(i); firstderivative(i,3)=NaN; end for i=orig_length+1:length(y) firstderivative(i,1)=NaN; firstderivative(i,3)=NaN; end

firstderivative end

other function: using center difference

function [firstdiff]= firstcentdiff( x,y ) %this function will find the first derivative using the center difference %method l=length(x); for n=1:l-1 func(n,1)=( x(n+1)+x(n))/2; %%% mid point value func(n,2)=(y(n+1)-y(n))/(2*(x(n+1)-x(n))); %%% first derivatives using cetral difference end firstdiff=func

end