Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-5+2*x)^2
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Limit of 4-6*x+2*x^4
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Limit of (2-x)^(3*x/(-1+x))
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Limit of (-3+x-6*x^2+2*x^3)/(-3+x)
- Graphing y =:
- log(x)^x
- Derivative of:
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log(x)^x
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Identical expressions
- log(x)^x
- logarithm of (x) to the power of x
- log(x)x
- logxx
- logx^x
Limit of the function log(x)^x
The solution
You have entered
[src]
x lim log (x) x->0+
$$\lim_{x \to 0^+} \log{\left(x \right)}^{x}$$
Limit(log(x)^x, x, 0)
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
One‐sided limits
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x lim log (x) x->0+
$$\lim_{x \to 0^+} \log{\left(x \right)}^{x}$$
1
$$1$$
= (1.00048226867183 + 0.000790877997040114j)
x lim log (x) x->0-
$$\lim_{x \to 0^-} \log{\left(x \right)}^{x}$$
1
$$1$$
= (0.999474651596538 - 0.000654397275377553j)
= (0.999474651596538 - 0.000654397275377553j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \log{\left(x \right)}^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(x \right)}^{x} = 1$$
$$\lim_{x \to \infty} \log{\left(x \right)}^{x} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(x \right)}^{x} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(x \right)}^{x} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(x \right)}^{x} = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(x \right)}^{x} = 1$$
$$\lim_{x \to \infty} \log{\left(x \right)}^{x} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(x \right)}^{x} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(x \right)}^{x} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(x \right)}^{x} = 0$$
More at x→-oo
Numerical answer
[src]
(1.00048226867183 + 0.000790877997040114j)
(1.00048226867183 + 0.000790877997040114j)
The graph