ex: ln lim x-> 0+ x^(sin x), y=x^(sin x)
using L'Hopital's Rule, the book says the answer is 1 but i don't know how to get to this answer
Thanks so much!
Looking at the individual functions, we see that both approach 0 as X approaches zero from the left. This would be an indeterminate power, of the form and thus we have to use L'hopital's rule.
To solve this we first take the natural logarithim of our function:
Which then gives us:
This then becomes an indeterminate product of the form
Do you see what to do at this point?
Hmmm, I believe he is asking if he can write
is equal to , which is of course no. I'm thinking OP is applying limit rearrangment of the type:
is the same as
The first way of writing it is how we want to set it up.
His second question is can he write it like this:
Which is the proper way to write it, but not using the logic he used. I apologize OP for not writing out the limit notation, as I just assumed you realized where they went.