# max $\sin(x)/x$ without derivative

Showing $max(\frac{sin(x)}{x})=1$ is straight forward using l'hopital's rule. Is there another way to evaluate without using l'hopital's rule

• It is not straightforward, it is circular. – DanielC Sep 18 '18 at 22:01
• Do you mean Sup(sin x/x)? – gimusi Sep 18 '18 at 22:03
• It's pretty easy using the Taylor series, but there is some sense it which is, as DanielC calls l'Hopital's rule, circular. – Acccumulation Sep 18 '18 at 22:19

## 1 Answer

HINT

To prove that $\sup\left(\frac{\sin x}x\right)=1$ we can proceed showing that

• $\frac{\sin x}x$ is even and not defined at $x=0$ then we can consider $x>0$
• $\lim_{x\to 0} \frac{\sin x}x=1$
• $g(x)=x-\sin x >0$ for $x>0$

Refer to the related