Thread: limit 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.

Originally Posted by harunulubey

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

What is a 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

thank you Hollywood I guess unique not migue thanks for your help...

And thank you Plato for your interest