easy limit problem

**IronMan21** · May 26th 2009, 04:59 PM

What is the limit as x-> infinity of arcsec(x)

**pickslides** · May 26th 2009, 05:43 PM

$y = arcsec(x)$ has $x \in [-1,1]$ therefore can it approach infinity?

**IronMan21** · May 26th 2009, 05:54 PM

so the limit does not exist?

**pickslides** · May 26th 2009, 05:56 PM

I think not.

**skeeter** · May 26th 2009, 06:11 PM

Originally Posted by IronMan21

What is the limit as x-> infinity of arcsec(x)

domain of $y = arcsec(x) = \arccos\left(\frac{1}{x}\right)$ is $(-\infty,-1] \cup [1, \infty)$

the limit as $x \to \infty$ is $\frac{\pi}{2}$

note the graph ...

**pickslides** · May 26th 2009, 06:22 PM

I was under the impression that

$y = arcsec(x) = \frac{1}{arccos(x)}$

**IronMan21** · May 27th 2009, 05:09 PM

I have one more question. If the limit was approaching negative infinity, wouldn't the answer also be pi/2? But that wouldn't make sense right?

**skeeter** · May 27th 2009, 05:12 PM

Originally Posted by IronMan21

I have one more question. If the limit was approaching negative infinity, wouldn't the answer also be pi/2? But that wouldn't make sense right?

look at the graph

**IronMan21** · May 27th 2009, 05:17 PM

wow im so stupid thanks

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