Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^2*(1/3-cos(8*x)/3)
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Limit of (9-x)/(-3+x^3)
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Limit of (8-7*x)/(-5-4*x+6*x^2)
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Limit of (7*x+8*x^3)/(4-x)
- Integral of d{x}:
- x^(-x)
- Graphing y =:
- x^(-x)
- Derivative of:
- x^(-x)
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Identical expressions
- x^(-x)
- x to the power of ( minus x)
- x(-x)
- x-x
- x^-x
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Similar expressions
- (1+1/x)^(-x)
- x^y-y^y-x^(-x)*y^x
- ((1-2*x)/(3-2*x))^(-x)
- (1+x)^x*(1-x)^(-x)
- x^(-x)*factorial(2*x)
- x^(x)
Limit of the function x^(-x)
The solution
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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} x^{- x} = 0$$
$$\lim_{x \to 0^-} x^{- x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{- x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{- x} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{- x} = 1$$
More at x→1 from the right
More at x→-oo
$$\lim_{x \to 0^-} x^{- x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{- x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{- x} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{- x} = 1$$
More at x→1 from the right
False
More at x→-oo
The graph