Question about limit.

Show that the equation cosx=2x has a migue solution x∈r.

if you know anything this question I want to hear your idea.

I can't understood migue solution.Have you any idea about this solution I'm waiting.

Thank you.

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- Nov 28th 2012, 05:54 AMharunulubeylimit equation (migue solution)
Question about limit.

Show that the equation cosx=2x has a migue solution x∈r.

if you know anything this question I want to hear your idea.

I can't understood migue solution.Have you any idea about this solution I'm waiting.

Thank you. - Nov 28th 2012, 07:03 AMPlatoRe: limit equation (migue solution)
- Nov 28th 2012, 07:47 AMhollywoodRe: limit equation (migue solution)
I think he means a unique solution.

The derivative of $\displaystyle f(x)=2x-\cos{x}$ is $\displaystyle 2+\sin{x}$, which is always positive, so the function is increasing. Also, $\displaystyle f(x)<0$ for large negative values of x and $\displaystyle f(x)>0$ for large positive values of x. So there is exactly one $\displaystyle x\in\mathbb{R}$ where it is zero, and that is a unique solution to $\displaystyle 2x=\cos{x}$.

- Hollywood - Nov 28th 2012, 09:52 AMharunulubeyRe: limit equation (migue solution)
thank you Hollywood I guess unique not migue thanks for your help...

- Nov 28th 2012, 09:53 AMharunulubeyRe: limit equation (migue solution)
And thank you Plato for your interest