Learn how to solve problems step by step online. Find the limit of (n^(1/2))/log(n) as n approaches infinity. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. Divide fractions \frac{\sqrt{n}}{\frac{\ln\left(n\right)}{\ln\left(10\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. If we directly evaluate the limit \lim_{n\to\infty }\left(\frac{\ln\left(10\right)\sqrt{n}}{\ln\left(n\right)}\right) as n tends to \infty , we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.

Find the limit of (n^(1/2))/log(n) as n approaches infinity