I have to find the following:
limit as x goes to 0 of x^sin(x)
I know that I get an indeterminate form 0^0 but what do I do from there to find the actual limit? I know the answer should be equal to 1, but how do I set up the problem to get that? Do I use l'hopitals? And if so.. how?
So let's consider
Now we can apply that L'hospital's rule to get
And via another LH Rule
So the ln of the limit=0 so what number do we plug into ln to get 0? The answer is 1
There's gotta be a better way, but this is what I came up with....