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Homework Statement
[tex] lim_{x->0} (1+ sin5x)^{cotx} [/tex]
Homework Equations
that's the problem.. I don't know :s
The Attempt at a Solution
can't think of any theorems or any methods I could use here.. what should I do? thank you
Here's the situation. You have y = (1 + sin5x)^{cotx}. Taking the natural log of both sides gives:thanks for the reply, I don't really understand the meaning behind doing ln(lim x -> 0 y) versus lim x-> 0 ln(y) when I'll just ln( y) either way?
Where are you getting cos(x)? The exponent is cot(x), not cos(x).also, what kind of identity should I use for my cos x to get my 0/0? I tried sqrt(1-sin^2x) and playing around with the difference of squares, but it didn't work so well.
You're being very sloppy. This is the second time you have mentioned ln(1 + sinx). It's ln(1 + sin(5x)). The product is cot(x)*ln(1 + sin5x). Can you think of a way to write this as a quotient suitable for use in L'Hopital's Rule, rather than a product?I feel like I might run into trouble with my ln(1+sinx) also, since that equals to zero, the product still might not go to zero, but I'll have to find a way around it. :S
thanks for the help!