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I have no problems finding first solution (both: $b \to 0$ and $b \to \infty$). My solutions on photos. I got stuck trying to find solution when $x \to \infty$. As I think, solution for $x$ will have $n$ in formula. I've no idea how to do this part.

I made all hard calculations using wolfram mathematica.

Тyma Gaidash
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Resha
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  • I've edited your post to use LaTeX markup for the formulas. If you'd like, you can read about how to do this here: http://meta.math.stackexchange.com/a/117/5531 and here: http://meta.math.stackexchange.com/q/5020/5531 – Antonio Vargas Apr 24 '14 at 15:22
  • You may also be interested in this question: http://math.stackexchange.com/q/719244/5531 and this question: http://math.stackexchange.com/q/110256/5531 – Antonio Vargas Apr 24 '14 at 15:23

1 Answers1

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Try replacing $x$ by $x+n\pi$ in the formula, so

$$ \frac{b}{x} = \tan x $$

becomes

$$ \frac{b}{x+n\pi} = \tan(x+n\pi) = \tan x. $$

Then it's still true in this new equation that $x \to 0$ as $b \to 0$ and $x \to \pi/2$ as $b \to \infty$, so you can use the same method you used to find the first solution.

Antonio Vargas
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