Limit Question

**Chandru1** · June 21st 2009, 02:55 AM

Given that $\Biggl| \cos^{-1} \biggl( \frac{1}{n} \biggr) \Biggr|< \frac{\pi}{2}$ evaluate:

$\lim_{n \to \infty} \frac{2}{\pi} (n+1) \cos^{-1} \biggl(\frac{1}{n} \biggr) -n$

**NonCommAlg** · June 21st 2009, 07:31 PM

Originally Posted by Chandru1

Given that $\Biggl| \cos^{-1} \biggl( \frac{1}{n} \biggr) \Biggr|< \frac{\pi}{2}$ evaluate:

$\lim_{n \to \infty} \frac{2}{\pi} (n+1) \cos^{-1} \biggl(\frac{1}{n} \biggr) -n$

put $n=\sec t.$ then you'll have a simple limit $\lim_{t \to\frac{\pi}{2}}\frac{2t(1+\cos t) - \pi}{\pi \cos t}=1-\frac{2}{\pi},$ by applying L'Hopital once.

Thread: Limit Question

LinkBack

Thread Tools

Display

Limit Question

Similar Math Help Forum Discussions

Two variable limit question (Question/Solution/Answer included)

limit question on a limit comparison test problem.

limit question

Another Limit Question

Another limit question

Search Tags