Mister Exam

# Limit of the function sqrt(x)*log(x)

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### The solution

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lim \\/ x *log(x)/
x->oo              
$$\lim_{x \to \infty}\left(\sqrt{x} \log{\left(x \right)}\right)$$
Limit(sqrt(x)*log(x), x, 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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\sqrt{x} \log{\left(x \right)}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\sqrt{x} \log{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sqrt{x} \log{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sqrt{x} \log{\left(x \right)}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sqrt{x} \log{\left(x \right)}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sqrt{x} \log{\left(x \right)}\right) = \infty i$$
More at x→-oo
Rapid solution [src]
oo
$$\infty$$
The graph