Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+3*x)^(5/x)
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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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Limit of e^(1+3*x)*(-1+x)
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Identical expressions
- (one +x)^(two / three)-(- one +x)^(two / three)
- (1 plus x) to the power of (2 divide by 3) minus ( minus 1 plus x) to the power of (2 divide by 3)
- (one plus x) to the power of (two divide by three) minus ( minus one plus x) to the power of (two divide by three)
- (1+x)(2/3)-(-1+x)(2/3)
- 1+x2/3--1+x2/3
- 1+x^2/3--1+x^2/3
- (1+x)^(2 divide by 3)-(-1+x)^(2 divide by 3)
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Similar expressions
- (1+x)^(2/3)-(-1-x)^(2/3)
- (1-x)^(2/3)-(-1+x)^(2/3)
- (1+x)^(2/3)-(1+x)^(2/3)
- (1+x)^(2/3)+(-1+x)^(2/3)
Limit of the function (1+x)^(2/3)-(-1+x)^(2/3)
The solution
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/ 2/3 2/3\ lim \(1 + x) - (-1 + x) / x->oo
$$\lim_{x \to \infty}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right)$$
Limit((1 + x)^(2/3) - (-1 + 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
$$\lim_{x \to \infty}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 0$$
$$\lim_{x \to 0^-}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 1 - \left(-1\right)^{\frac{2}{3}}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 1 - \left(-1\right)^{\frac{2}{3}}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 2^{\frac{2}{3}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 2^{\frac{2}{3}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 1 - \left(-1\right)^{\frac{2}{3}}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 1 - \left(-1\right)^{\frac{2}{3}}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 2^{\frac{2}{3}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 2^{\frac{2}{3}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \left(x - 1\right)^{\frac{2}{3}} + \left(x + 1\right)^{\frac{2}{3}}\right) = 0$$
More at x→-oo
The graph