Mister Exam

# Limit of the function log(n)/sqrt(n)

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### The solution

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     /log(n)\
lim |------|
n->oo|  ___ |
\\/ n  /
$$\lim_{n \to \infty}\left(\frac{\log{\left(n \right)}}{\sqrt{n}}\right)$$
Limit(log(n)/(sqrt(n)), n, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Rapid solution [src]
0
$$0$$
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(\frac{\log{\left(n \right)}}{\sqrt{n}}\right) = 0$$
$$\lim_{n \to 0^-}\left(\frac{\log{\left(n \right)}}{\sqrt{n}}\right) = \infty i$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{\log{\left(n \right)}}{\sqrt{n}}\right) = -\infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{\log{\left(n \right)}}{\sqrt{n}}\right) = 0$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{\log{\left(n \right)}}{\sqrt{n}}\right) = 0$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{\log{\left(n \right)}}{\sqrt{n}}\right) = 0$$
More at n→-oo
The graph