Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3*e^(4*x)-2*e^(-x)+5*e^(2*x))/(-4*sqrt(1+5*x)+4*cos(3*x)+5*sin(2*x))
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Limit of (x/2)^(5/(-2+x))
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Limit of (-4+x^2)/(6+x^2+5*x)
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Limit of ((-1+x)/(1+x))^(1+x)
- Graphing y =:
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2/x^(2/3)
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Identical expressions
- two /x^(two / three)
- 2 divide by x to the power of (2 divide by 3)
- two divide by x to the power of (two divide by three)
- 2/x(2/3)
- 2/x2/3
- 2/x^2/3
- 2 divide by x^(2 divide by 3)
Limit of the function 2/x^(2/3)
The solution
You have entered
[src]
/ 2 \
lim |----|
x->0+| 2/3|
\x /
$$\lim_{x \to 0^+}\left(\frac{2}{x^{\frac{2}{3}}}\right)$$
Limit(2/x^(2/3), 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
$$\lim_{x \to 0^-}\left(\frac{2}{x^{\frac{2}{3}}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{\frac{2}{3}}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{\frac{2}{3}}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{\frac{2}{3}}}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
lim |----|
x->0+| 2/3|
\x /
$$\lim_{x \to 0^+}\left(\frac{2}{x^{\frac{2}{3}}}\right)$$
oo
$$\infty$$
= 56.7128266713576
/ 2 \
lim |----|
x->0-| 2/3|
\x /
$$\lim_{x \to 0^-}\left(\frac{2}{x^{\frac{2}{3}}}\right)$$
3 ____ -oo*\/ -1
$$- \infty \sqrt[3]{-1}$$
= (-28.3564133356788 - 49.1147486178194j)
= (-28.3564133356788 - 49.1147486178194j)
The graph