I have to calculate the following limit lim x → + ∞ x ln ...
I have to calculate the following limit
Answer & Explanation
is infinity even though the denominator does not converge.
The real problem with your function is that it isn’t defined for all of But if f is a function defined on a subset of with no real upper bound, we can still define
In your case, you easily get, where f is defined, and
since in the domain of f
Since this means
The quotient is undefined when . Otherwise, , and therefore
it follows from (1) that