Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3*x+14*x^2)/(1+2*x+7*x^2)
- Limit of log(factorial(n))/log(n^n)
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Limit of acot(3*x)
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Limit of 15
- Derivative of:
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x^x
- Integral of d{x}:
- x^x
- Graphing y =:
- x^x
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Identical expressions
- x^x
- x to the power of x
- xx
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Similar expressions
- ((1+2*x)/(2+2*x))^x
- (8-7*x)^(x/(-1+x))
- ((-1+3*x)/(3*x))^x
- cosh(x)^(x^(-2))
- cos(2/x)^(x^2)
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
$$\lim_{x \to \infty} x^{x} = \infty$$
$$\lim_{x \to 0^-} x^{x} = 1$$
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
$$\lim_{x \to -\infty} x^{x} = \infty$$
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
$$\lim_{x \to -\infty} x^{x} = \infty$$
More at x→-oo
The graph