Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-1+x)/(x+x^2)
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Limit of log(-5+x)/log(e^x-e^5)
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Limit of (-exp(-x)-2*x+exp(x))/(x-sin(x))
- Limit of e^(-n*x)/n
- Derivative of:
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x^(-2/3)
- Integral of d{x}:
- x^(-2/3)
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Identical expressions
- x^(- two / three)
- x to the power of ( minus 2 divide by 3)
- x to the power of ( minus two divide by three)
- x(-2/3)
- x-2/3
- x^-2/3
- x^(-2 divide by 3)
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Similar expressions
- x^(2/3)
Limit of the function x^(-2/3)
The solution
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1
lim ----
x->oo 2/3
x
$$\lim_{x \to \infty} \frac{1}{x^{\frac{2}{3}}}$$
Limit(x^(-2/3), 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
$$\lim_{x \to \infty} \frac{1}{x^{\frac{2}{3}}} = 0$$
$$\lim_{x \to 0^-} \frac{1}{x^{\frac{2}{3}}} = - \infty \sqrt[3]{-1}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x^{\frac{2}{3}}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x^{\frac{2}{3}}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{\frac{2}{3}}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x^{\frac{2}{3}}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{x^{\frac{2}{3}}} = - \infty \sqrt[3]{-1}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x^{\frac{2}{3}}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x^{\frac{2}{3}}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{\frac{2}{3}}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x^{\frac{2}{3}}} = 0$$
More at x→-oo
The graph