Find the limit:

lim x-> 0+ tan ^-1 (lnx) =?

I have no ide where to begin here? Can someone explain this in simple steps? Please, do not just give me another limit equation...

Thanks

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- Jan 12th 2010, 12:10 PMDBAFind the limit - inverse trig
Find the limit:

lim x-> 0+ tan ^-1 (lnx) =?

I have no ide where to begin here? Can someone explain this in simple steps? Please, do not just give me another limit equation...

Thanks - Jan 12th 2010, 12:54 PMCalculus26
lim x-> 0+ tan ^-1 (lnx) = tan^(-1)[lim(ln(x)] = tan^(-1)(-infinity)= -pi/2

- Jan 12th 2010, 12:54 PMDrexel28
- Jan 12th 2010, 01:23 PMgalactus
Let's do something wacky and fun(Wink).

Note that

Use L'hopital on the inside:

The limit tends to -1 and we get

So, we get - Jan 12th 2010, 01:54 PMDBA
- Jan 12th 2010, 01:56 PMDBA
- Jan 12th 2010, 01:58 PMDBA
- Jan 12th 2010, 02:00 PMCalculus26
yes in general

limf(g) = f(lim(g)) at a point if x = a if g is continuous at x = a and the limf exists at g(a) - Jan 12th 2010, 02:01 PMgalactus
I am sorry. Perhaps I shouldn't have done that. Just having fun. You will learn L'Hopital in time. It's a handy tool.

There are easier ways to go about it. Take note that