Trigonometric Limits

Posted December 9th, 2009 by alpha

Find: $\mathop{\lim}\limits_{n\to \infty}n sin (\frac{\pi}{4n})cos(\frac{\pi}{4n})=\frac{\pi}{4}$

Comments

On December 11th, 2009 Structure says:

$\lim_{n\to \infty}n sin (\frac{\pi}{4n})cos(\frac{\pi}{4n})=\lim_{n\to \infty}\frac{sin (\frac{\pi}{4n})}{\frac{1}{n}}=\frac{\pi}{4}$

$\lim_{n\to \infty}cos(\frac{\pi}{4n})=1$

and

$\lim_{x\to 0}\frac{\sin ax}{x}=a$