# hard limit problem involving a trig. exponent

• April 4th 2013, 01:02 PM
Lambin
hard limit problem involving a trig. exponent
PROBLEM:

$\lim_{x\to\(\pi^+)}{(1+3sinx)^{cot(x)}}$

ATTEMPT:

Does L'Hopital's Rule apply work for this problem? I don't think so, because it is not in the appropriate indeterminate form; for, it would be $1^\infty$. But I don't know any elementary methods that would be appropriate here, nor any limit properties. :/
• April 4th 2013, 01:35 PM
ebaines
Re: hard limit problem involving a trig. exponent
Yes, L'Hospital's works. Try this - take the log of the expression, and you get:

$\lim ( \ln (1+3 \sinx)^{cotx}))= \lim ( \frac { \cos x \ln (1+3\sin x)}{\sin x})$

Now use L'Hospital's, and you shoud find that this limit approahes a value, let's call it A. The the limit of the original problem is $e^A$.