- #1
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How do I find the first 10 positive solutions numerically?
$$
\tan x = \frac{1}{x}
$$
$$
\tan x = \frac{1}{x}
$$
How do you find the first positive solution? You tell US; do not ask us to tell you: read the forum rules.How do I find the first 10 positive solutions numerically?
$$
\tan x = \frac{1}{x}
$$
Where are you stuck?How do I find the first 10 positive solutions numerically?
$$
\tan x = \frac{1}{x}
$$
I am not good at numerical analysis. I haven't taken a course in it yet as well as in Matlab. I will be taking Matlab this spring and Numerical Analysis next fall. So when I know how to do it and use Matlab efficiently, I won't even ask you.How do you find the first positive solution? You tell US; do not ask us to tell you: read the forum rules.
RGV
Read post 3.Where are you stuck?
What have you tried?
After 490 posts, you should know the drill here at PF .
But here's one hint: One thing I would try is to take the reciprocal of both sides of that equation, giving you:[itex]\displaystyle \cot(x)=x[/itex]
Graph each side.
I have a graph of it. I don't know if the forum can handle tikz but here it isNumerically means approximately since this is a transcendental equation. Only some computer software would give you the results, I think.
http://www.wolframalpha.com/input/?i=Plot+y(x)+=+tan+x+-+1/x
You don't need to know how to use Matlab, etc. Just apply Newton's method, which you can do using a hand-held scientific calculator. If you have not ever seen Newton's method before, I would be very surprised.I am not good at numerical analysis. I haven't taken a course in it yet as well as in Matlab. I will be taking Matlab this spring and Numerical Analysis next fall. So when I know how to do it and use Matlab efficiently, I won't even ask you.
I tried using NSolve in Mathematica but that didn't work.Here are the graphs of y=x and y=cot(x), superimposed. (from WolframAlpha)
I don't have access to Mathematica (except through Wolfram Alpha) or to Matlab, but in Maple it is easy:I tried using NSolve in Mathematica but that didn't work.
I also tried
syms x
solve(tan(x)==1/x)
in Matlab and that just gave -263.
How can I do this in one of these programs?
This is what I wrote in post 3.
I can make graphs of this with the Tikz package and in Mathematica (that isn't the challenge here). How can I use Mathematica or Matlab to generate the first 10 positive solution?
Thanks. Hopefully in the spring when I take programming in Matlab I will be better at this.I don't have access to Mathematica (except through Wolfram Alpha) or to Matlab, but in Maple it is easy:
S:=fsolve(tan(x)=1/x,x=0..Pi/2),seq(fsolve(tan(x)=1/x,x=Pi/2+(i-1)*Pi..Pi/2+i*Pi),i=1..9);
S := 0.8603335890, 3.425618459, 6.437298179, 9.529334405,
12.64528722, 15.77128487, 18.90240996, 22.03649673,
25.17244633, 28.30964285
I'm sure it must be possible, even easy, to do the same thing in Mathematica.
RGV
Try using FindRoot instead.I tried using NSolve in Mathematica but that didn't work.
In[7]:= Plot[Tan[x]-1/x,{x,.01,30}]I tried using NSolve in Mathematica but that didn't work.
...
How can I do this in one of these programs?