Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
- Limit of log(factorial(n))
-
Limit of sqrt(x)*log(x)
- Limit of (x^4-a^4)/(x-a)
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Limit of sin(z)
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Identical expressions
- log(factorial(n))
- logarithm of (factorial(n))
- logfactorialn
Limit of the function log(factorial(n))
The solution
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lim log(n!) n->oo
$$\lim_{n \to \infty} \log{\left(n! \right)}$$
Limit(log(factorial(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
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty} \log{\left(n! \right)} = \infty$$
$$\lim_{n \to 0^-} \log{\left(n! \right)} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} \log{\left(n! \right)} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} \log{\left(n! \right)} = 0$$
More at n→1 from the left
$$\lim_{n \to 1^+} \log{\left(n! \right)} = 0$$
More at n→1 from the right
$$\lim_{n \to -\infty} \log{\left(n! \right)} = \log{\left(\left(-\infty\right)! \right)}$$
More at n→-oo
$$\lim_{n \to 0^-} \log{\left(n! \right)} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} \log{\left(n! \right)} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} \log{\left(n! \right)} = 0$$
More at n→1 from the left
$$\lim_{n \to 1^+} \log{\left(n! \right)} = 0$$
More at n→1 from the right
$$\lim_{n \to -\infty} \log{\left(n! \right)} = \log{\left(\left(-\infty\right)! \right)}$$
More at n→-oo