# limit equation (migue solution)

• Nov 28th 2012, 05:54 AM
harunulubey
limit equation (migue solution)
Show that the equation cosx=2x has a migue solution x∈r.

if you know anything this question I want to hear your idea.
Thank you.
• Nov 28th 2012, 07:03 AM
Plato
Re: limit equation (migue solution)
Quote:

Originally Posted by harunulubey
Question about limit. Show that the equation cosx=2x has a migue solution x∈r.

What is a migue solution ?
• Nov 28th 2012, 07:47 AM
hollywood
Re: 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 AM
harunulubey
Re: limit equation (migue solution)
thank you Hollywood I guess unique not migue thanks for your help...
• Nov 28th 2012, 09:53 AM
harunulubey
Re: limit equation (migue solution)
And thank you Plato for your interest