Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
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Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
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Limit of (-14+x^2-5*x)/(-6+x+2*x^2)
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Limit of (3+x^2+4*x)/(1+x^3)
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Identical expressions
- factorial(n)^(one /n)
- factorial(n) to the power of (1 divide by n)
- factorial(n) to the power of (one divide by n)
- factorial(n)(1/n)
- factorialn1/n
- factorialn^1/n
- factorial(n)^(1 divide by n)
Limit of the function factorial(n)^(1/n)
The solution
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n ____ lim \/ n! n->oo
$$\lim_{n \to \infty} n!^{1 \cdot \frac{1}{n}}$$
Limit(factorial(n)^(1/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
$$\lim_{n \to \infty} n!^{1 \cdot \frac{1}{n}} = \infty$$
$$\lim_{n \to 0^-} n!^{1 \cdot \frac{1}{n}} = e^{- \gamma}$$
More at n→0 from the left
$$\lim_{n \to 0^+} n!^{1 \cdot \frac{1}{n}} = e^{- \gamma}$$
More at n→0 from the right
$$\lim_{n \to 1^-} n!^{1 \cdot \frac{1}{n}} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} n!^{1 \cdot \frac{1}{n}} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} n!^{1 \cdot \frac{1}{n}} = 1$$
More at n→-oo
$$\lim_{n \to 0^-} n!^{1 \cdot \frac{1}{n}} = e^{- \gamma}$$
More at n→0 from the left
$$\lim_{n \to 0^+} n!^{1 \cdot \frac{1}{n}} = e^{- \gamma}$$
More at n→0 from the right
$$\lim_{n \to 1^-} n!^{1 \cdot \frac{1}{n}} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} n!^{1 \cdot \frac{1}{n}} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} n!^{1 \cdot \frac{1}{n}} = 1$$
More at n→-oo