1. The problem statement, all variables and given/known data
Find the limit:
[itex]lim_{x -> \infty}[n*(x^{\frac{1}{n}}-1)-ln(x)][/itex], for any n.
2. Relevant equations
L'Hopitals rule.
3. The attempt at a solution
I know that the ratio of the first expression over the last goes to zero, by L'Hopital, but unfortunately I now have a difference and not a quotient. Is it possible to transform it in some way to use L'Hopital?
Find the limit:
[itex]lim_{x -> \infty}[n*(x^{\frac{1}{n}}-1)-ln(x)][/itex], for any n.
2. Relevant equations
L'Hopitals rule.
3. The attempt at a solution
I know that the ratio of the first expression over the last goes to zero, by L'Hopital, but unfortunately I now have a difference and not a quotient. Is it possible to transform it in some way to use L'Hopital?
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