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

  • 1
    $\begingroup$ It is not straightforward, it is circular. $\endgroup$ – DanielC Sep 18 '18 at 22:01
  • $\begingroup$ Do you mean Sup(sin x/x)? $\endgroup$ – gimusi Sep 18 '18 at 22:03
  • $\begingroup$ It's pretty easy using the Taylor series, but there is some sense it which is, as DanielC calls l'Hopital's rule, circular. $\endgroup$ – Acccumulation Sep 18 '18 at 22:19


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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.