Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-9+x+6*x^2)/(7+5*x+8*x^2)
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Limit of 2+((5-x)/(6-x))^x
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Limit of 1/2-3*x+4*x^2
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Limit of -2*x+5*x^2+4*(1+x)/(-1+x)
- Derivative of:
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(1/x)^x
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Identical expressions
- (one /x)^x
- (1 divide by x) to the power of x
- (one divide by x) to the power of x
- (1/x)x
- 1/xx
- 1/x^x
- (1 divide by x)^x
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Similar expressions
- (x*sinh(1/x))^(x^2)
- (1+1/x)^x
Limit of the function (1/x)^x
The solution
You have entered
[src]
x
/1\
lim |-|
x->0+\x/
$$\lim_{x \to 0^+} \left(\frac{1}{x}\right)^{x}$$
Limit((1/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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(\frac{1}{x}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x}\right)^{x} = 1$$
$$\lim_{x \to \infty} \left(\frac{1}{x}\right)^{x} = 0$$
More at x→oo
$$\lim_{x \to 1^-} \left(\frac{1}{x}\right)^{x} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x}\right)^{x} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x}\right)^{x} = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x}\right)^{x} = 1$$
$$\lim_{x \to \infty} \left(\frac{1}{x}\right)^{x} = 0$$
More at x→oo
$$\lim_{x \to 1^-} \left(\frac{1}{x}\right)^{x} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x}\right)^{x} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x}\right)^{x} = \infty$$
More at x→-oo
One‐sided limits
[src]
x
/1\
lim |-|
x->0+\x/
$$\lim_{x \to 0^+} \left(\frac{1}{x}\right)^{x}$$
1
$$1$$
= 1.00136961801338
x
/1\
lim |-|
x->0-\x/
$$\lim_{x \to 0^-} \left(\frac{1}{x}\right)^{x}$$
1
$$1$$
= (0.998069004047152 - 0.000766163593756062j)
= (0.998069004047152 - 0.000766163593756062j)
The graph