Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-4*x)^(1/x)
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Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
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Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of 1/3+x/3
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Identical expressions
- (x^(- two))^(one /x)
- (x to the power of ( minus 2)) to the power of (1 divide by x)
- (x to the power of ( minus two)) to the power of (one divide by x)
- (x(-2))(1/x)
- x-21/x
- x^-2^1/x
- (x^(-2))^(1 divide by x)
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Similar expressions
- (x^(2))^(1/x)
Limit of the function (x^(-2))^(1/x)
The solution
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[src]
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/ 1
lim / --
x->oox / 2
\/ x
$$\lim_{x \to \infty} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}}$$
Limit((x^(-2))^(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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 1$$
$$\lim_{x \to 0^-} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x^{2}}\right)^{1 \cdot \frac{1}{x}} = 1$$
More at x→-oo
The graph