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 (-2+x^2-x)/(-2+x+3*x^2)
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Limit of (-1+sin(x))/cos(x)
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Limit of (-2*sin(x)+sin(2*x))/(x*log(cos(5*x)))
- Derivative of:
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x^(-1/3)
- Integral of d{x}:
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x^(-1/3)
- Sum of series:
- x^(-1/3)
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Identical expressions
- x^(- one / three)
- x to the power of ( minus 1 divide by 3)
- x to the power of ( minus one divide by three)
- x(-1/3)
- x-1/3
- x^-1/3
- x^(-1 divide by 3)
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Similar expressions
- x*atan((-1+x)^(-1/3))/(-1+x)
- x^(1/3)
- ((-4+3*x)/(2+3*x))^(-1/3+x/3)
Limit of the function x^(-1/3)
The solution
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1
lim -----
x->oo3 ___
\/ x
$$\lim_{x \to \infty} \frac{1}{\sqrt[3]{x}}$$
Limit(x^(-1/3), 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
$$\lim_{x \to \infty} \frac{1}{\sqrt[3]{x}} = 0$$
$$\lim_{x \to 0^-} \frac{1}{\sqrt[3]{x}} = - \infty \left(-1\right)^{\frac{2}{3}}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\sqrt[3]{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\sqrt[3]{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\sqrt[3]{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\sqrt[3]{x}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{\sqrt[3]{x}} = - \infty \left(-1\right)^{\frac{2}{3}}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\sqrt[3]{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\sqrt[3]{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\sqrt[3]{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\sqrt[3]{x}} = 0$$
More at x→-oo
The graph