what's the reason for getting an output at the point itself though it is not in range
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i have used taylor series to find the first derivative of the following function cos(x) and got 2 diffrent approximations ,
i wanted to check which one has more precision,
i started by understanding how to graph the function and its derviative wrote the 2 approximations for it, then tried to graph each graphs error , i have not yet added axis names and so on , but this graph
plot(x+h,approx_1(f,x,h),'*',x-h,approx_1(f,x,-h),'*') is for the first approximation of the value of the point
and the second plot(x+h,approx_2(f,x,h),'*',x-h,approx_2(f,x,-h),'*')
yet i get a number at the point it self though the range of h does not include 0 what may be the cause
,thanks for the guidness in advance
%testing a bit too much
f = @cos;
x = 1;
h=0:0.1:8*pi;
plot(x+h,f(x+h),'*',x-h,f(x-h),'*')
d_f =@(x) -sin(x);
exact = d_f(x);
h=0:0.1:8*pi;
hold on
plot(x+h,d_f(x+h),'*',x-h,d_f(x-h),'*')
exact = d_f(x);
hold off
d_f(1)
f(1)
%testing near the point of interest but closer
h2=0:0.001:10^-2
plot(x+h2,f(x+h2),'*',x-h2,f(x-h2),'*')
plot(x+h2,d_f(x+h2),'*',x-h2,d_f(x-h2),'*')
%identifiy
approx_1=@(f, x, h) (f(x + h) - f(x))./ h;
approx_2=@(f, x, h) (f(x + h) - f(x-h)) ./ (2*h);
d_f(1)
h = linspace(10^-15,10^-1,20)
plot(x+h,approx_1(f,x,h),'*',x-h,approx_1(f,x,-h),'*')
plot(x+h,approx_2(f,x,h),'*',x-h,approx_2(f,x,-h),'*')
v_1_up=approx_1(f,x,h)-d_f(1)
v_2_up=approx_2(f,x,h)-d_f(1)
v_1_down=approx_1(f,x,-h)-d_f(1)
v_2_down=approx_2(f,x,-h)-d_f(1)
%plot(h,v_1_up,'*',h,v_1_down,'*')
%plot(h,v_2_up,'*',h,v_2_down,'*')
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Answers (1)
Walter Roberson
on 1 Jul 2024
h=0:0.1:8*pi;
approx_1=@(f, x, h) (f(x + h) - f(x)) / h;
Your h is a vector. You need to use ./ instead of /
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