solve x*tan(x)-0.5=0

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rakesh kumar
rakesh kumar 2022-3-27
编辑： Sam Chak 2022-3-28
I am again stuck with similar question which I asked earlier. I am trying to solve x*tan(x)-0.5=0,but when i cross checked the result I am getting very different results.
syms x
n=10;
for n = 1:2:n
x1 = (n-1/2)*pi;
x2 = (n)*pi;
w(n) = double(vpasolve(x*tan(x)-0.5 == 0,x,[x1 x2]))
check(n)=w(n)*tan(w(n))-0.5
end
I am getting
w =
1.5708 0 7.8540 0 14.1372 0 20.4204 0 26.7035
check =
1.0e+16 *
2.5653 0 2.5653 0 2.5653 0 -2.0830 0 -3.6311. I am unable to find my mistake.

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采纳的回答

Torsten
Torsten 2022-3-27
编辑：Torsten 2022-3-27
x1=0:0.1:1.3;
y1=x1.*tan(x1)-0.5;
x2=2:0.1:4.1;
y2=x2.*tan(x2)-0.5;
x3=5.5:0.1:6.9;
y3=x3.*tan(x3)-0.5;
plot(x1,y1,x2,y2,x3,y3)
So was your choice of x1 and x2 resonable ?
Here you get the asymptotic distribution of the zeros of your function in order to make a proper choice of x1 and x2:
https://math.stackexchange.com/questions/1238520/how-to-find-asymptotic-expansions-of-all-real-roots-of-x-tanx-epsilon-1
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rakesh kumar
rakesh kumar 2022-3-28
Thanks once again. I ran your code and its giving the perfect answer. You people are really great!
Sam Chak
Sam Chak 2022-3-28
编辑：Sam Chak 2022-3-28
@Torsten
Learned something today. Thank you.
@rakesh kumar
Also thanks for showing an interesting question.

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