Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
- Limit of (1/factorial(x))^(1/x)
- Limit of (1+cos(3*x))^(1/cos(x))
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Limit of (1-cos(2*x))/(1-cos(4*x))
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Limit of (1-4*x)/(-2+5*x)
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Identical expressions
- (one /factorial(x))^(one /x)
- (1 divide by factorial(x)) to the power of (1 divide by x)
- (one divide by factorial(x)) to the power of (one divide by x)
- (1/factorial(x))(1/x)
- 1/factorialx1/x
- 1/factorialx^1/x
- (1 divide by factorial(x))^(1 divide by x)
Limit of the function (1/factorial(x))^(1/x)
The solution
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/ 1
lim x / --
x->oo\/ x!
$$\lim_{x \to \infty} \left(\frac{1}{x!}\right)^{\frac{1}{x}}$$
Limit((1/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
$$\lim_{x \to \infty} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = 0$$
$$\lim_{x \to 0^-} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = e^{\gamma}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = e^{\gamma}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = e^{\gamma}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = e^{\gamma}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x!}\right)^{\frac{1}{x}} = 1$$
More at x→-oo