Francisco P. answered • 10/06/14
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Well-Versed in Calculus
If you look at the tan(x) function, it goes through zero with a slope of 1 when x = 0.
So the limit as as x approaches 0+ for arctan(x) is a little bit positive since arctan(0) = 0.
The limit of ln(arctan(x)) is then -∞ since ln(x) approaches -∞ on the positive side of x = 0.
Byron S.
You know that lim(x->0+) arctan(x) = 0+
You can then rewrite your original limit as lim(u->0+) ln(u) where u = arctan(x)
From the behavior of ln(u), you know that this limit is -∞.
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10/06/14
Forrest C.
10/06/14