Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sqrt(x)*log(x)
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Limit of sin(z)
- Limit of sin(factorial(x))
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Limit of sin(sqrt(x))/sqrt(x)
- Derivative of:
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sqrt(x)*log(x)
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Identical expressions
- sqrt(x)*log(x)
- square root of (x) multiply by logarithm of (x)
- √(x)*log(x)
- sqrt(x)log(x)
- sqrtxlogx
Limit of the function sqrt(x)*log(x)
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
$$\lim_{x \to 0^-}\left(\sqrt{x} \log{\left(x \right)}\right) = 0$$
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
The graph