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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
/
factorial(n)
/
log(factorial(n))
Limit of the function log(factorial(n))
at
→
Calculate the limit!
For end points:
---------
From the left (x0-)
From the right (x0+)
The graph:
from
to
Enter:
{
piecewise-defined function here
The solution
You have entered
[src]
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
Rapid solution
[src]
oo
$$\infty$$
Expand and simplify
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
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