That L'Hospital's rule leads to the same ratio is natural since, as you pointed out, the derivative of again contains .
One can easily do without L'Hospital's rule here since is a constant.
I have two functions:
and
I have to prove it its big-Oh/theta/omega
I have to use the limit method where:
limit n going to infinity of
Then L'Hospital's rule, but when I take the derivatives of both and cancel out everything I just get what I was left with before. Am I doing something wrong? Am I not taking the derivative correctly?
I was using and chain rule.
Can someone help me to clarify this?
It is. However, for instance, is also infinity over infinity, and yet this fraction not only tends to 3/2, but is equal to 3/2.
I personally was taught to avoid L'Hopital's rule and to study the function's behavior. Often this results in better understanding of why the limit is what it is.