Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of -2+x^3+6*x
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Limit of (-15+x^2-2*x)/(-15-7*x+2*x^2)
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Limit of (1+x)^(3/2)/(2+x)^(3/2)
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Limit of (-1+tan(x)^(1/3))/(-1+log(x)/log(pi/4))
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Identical expressions
- factorial(x)^(- one /x)
- factorial(x) to the power of ( minus 1 divide by x)
- factorial(x) to the power of ( minus one divide by x)
- factorial(x)(-1/x)
- factorialx-1/x
- factorialx^-1/x
- factorial(x)^(-1 divide by x)
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Similar expressions
- factorial(x)^(1/x)
Limit of the function factorial(x)^(-1/x)
The solution
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-1
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x
lim x!
x->oo
$$\lim_{x \to \infty} x!^{- \frac{1}{x}}$$
Limit(factorial(x)^(-1/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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} x!^{- \frac{1}{x}} = 0$$
$$\lim_{x \to 0^-} x!^{- \frac{1}{x}} = e^{\gamma}$$
More at x→0 from the left
$$\lim_{x \to 0^+} x!^{- \frac{1}{x}} = e^{\gamma}$$
More at x→0 from the right
$$\lim_{x \to 1^-} x!^{- \frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x!^{- \frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x!^{- \frac{1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} x!^{- \frac{1}{x}} = e^{\gamma}$$
More at x→0 from the left
$$\lim_{x \to 0^+} x!^{- \frac{1}{x}} = e^{\gamma}$$
More at x→0 from the right
$$\lim_{x \to 1^-} x!^{- \frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x!^{- \frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x!^{- \frac{1}{x}} = 1$$
More at x→-oo