Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
- Limit of log(factorial(n))
- Limit of tanh(x)
- Limit of cot(pi*x)*sin(x)/(2*sec(x))
- Limit of sin(z)
-
Identical expressions
- log(factorial(n))
- logarithm of (factorial(n))
- logfactorialn
-
Similar expressions
- log(factorial(n))/log(n^n)
- log(factorial(n))/(n^2*log(2))
- log(factorial(n))/(n*log(n))
-
Expressions with functions
- Logarithm log
- log(log(x))
- log(2*x)*log(-1+2*x)
- log(cosh(x))/log(cos(x))
- log(sin(x))/log(sin(2*x))
- log(tan(x))*tan(x)
- factorial
- factorial(n)^2/factorial(2*n)
- factorial(x)
- factorial(x)/(3^x+x^3)
- factorial(x)/(1+2*x)
- factorial(1+n)
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