Math Help - I'Hopital's rule

1. I'Hopital's rule

Use I'Hopital's rule to find the limit of the sequence

2. That is overkilling it.

$n\sin \frac{1}{n} = \frac{\sin \frac{1}{n}}{\frac{1}{n}}$.

3. thanks for your prompt answer, but how did pie get in?

4. Hello,

Originally Posted by al1850
Where do you see any pie ?
Or any $\pi$ ?

5. Hi

Maybe in the ThePerfectHacker's signature ?
$\boxed{ -\sin \frac{\pi}{7} + \sin \frac{2\pi}{7} + \sin \frac{3\pi}{7} + \sin \frac{4\pi}{7}+\sin \frac{5\pi}{7} - \sin \frac{6\pi}{7} = \sqrt{7} }
$

6. Haha ! That's funny

7. oh man, that's your signature? I thought that was the answer to the I'Hopital's rule question. lol

8. So is (sin 1/n)/(1/n) the answer?

9. $\lim_{n\to\infty}\frac{\sin\frac{1}{n}}{\frac{1}{n }}$

Substitute $a=\frac{1}{n}$.

10. And remember the definition of the derivative :

$\lim_{x \to x_0} \frac{f(x)-f(x_0)}{x-x_0}=f'(x_0)$

Here, $f(x)=\sin(x)$

Take $x_0=0$

Or else, apply l'Hôpital's rule