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log(x)/sqrt(x)
Limit of the function/ log(x)/sqrt(x)

Limit of the function log(x)/sqrt(x)

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     /log(x)\
 lim |------|
x->oo|  ___ |
     \\/ x  /
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right)$$ 
Limit(log(x)/sqrt(x), x, oo, dir='-')
Lopital's rule
We have indeterminateness of type
oo/oo,

i.e. limit for the numerator is
$$\lim_{x \to \infty} \log{\left(x \right)} = \infty$$
and limit for the denominator is
$$\lim_{x \to \infty} \sqrt{x} = \infty$$
Let's take derivatives of the numerator and denominator until we eliminate indeterninateness.
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \log{\left(x \right)}}{\frac{d}{d x} \sqrt{x}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{2}{\sqrt{x}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{2}{\sqrt{x}}\right)$$
=
$$0$$
It can be seen that we have applied Lopital's rule (we have taken derivatives with respect to the numerator and denominator) 1 time(s)
The graph
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Rapid solution [src] 
0
$$0$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right) = \infty i$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→-oo
The graph
Limit of the function log(x)/sqrt(x)
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