Limit of logarithmic function using l'Hospital How can I find the following limit: lim_(x-oo)(ln(1+alpha x))/(ln(ln(1+e^(beta x)))) where alpha, beta in RR^+
Melissa Walker
Answered question
2022-11-18
Limit of logarithmic function using l'Hospital How can I find the following limit:
where My first guess was to use l'Hospital:
But what can I do now? Is my approach correct or is there a simpler method? Edit:
Applying L'Hospital a second time on the first fraction,
Now let's apply L'Hospital one final time:
Is this correct?
Answer & Explanation
martinmommy26nv8
Beginner2022-11-19Added 16 answers
The first application of l'Hôpital's theorem gives
Now,
so we just need to compute
You don't need anything new for this limit, because you have just computed the reciprocal.
Alfredo Cooley
Beginner2022-11-20Added 4 answers
We can proceed as follows
Here we have used the fact that and as we have , , and