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?
For questions similar to this, where the exponent plays a key role, it helps to consider an entirely different question, namely the logarithm of the limit
So let's consider
Now we can apply that L'hospital's rule to get
And via another LH Rule
=0
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....