find the root of the equation x=tanx using regular falsi method
Answers
Answer:
I needed to find, using the bisection method, the first positive value that satisfy x=tan(x). So I went to Scilab, I wrote the bisection method and I got 1.5707903. But after some reasoning I came to the conclusion that this value is wrong:
tan(1.5707903)≈1.6x105. Not even close to 1.5707903.
Forget for a moment the above. x=tan(x) is actually to find fixed points of f(x)=tan(x); (x,f(x)) must be in the line y=x. Here is the plot:plot(tan(x), x)
In (0,32π) I can only see a fixed point to the right of x=4, therefore 1.5707903 is wrong.
Here comes the interesting part. If you go to Wolfram Alpha and type x=tan(x), you will see 1.5708 in the Plot section:x = tan(x)
However there is no 1.5708 in the Numerical solutions section. Wolfram Alpha found 0,±4.49340945790906,….
But if you type tan(x)=x, you will not see 1.5708 in the Plot section!:tan(x) = x
To summarize:
Is 4.49340945790906 the first positive value that satisfy x=tan(x)?
Do you know why Wolfram Alpha is showing 1.5708 as a solution when you type x=tan(x) but not when you type tan(x)=x?
Step-by-step explanation:
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