Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (1-3*x^2+2*x^3)/(x^3+2*x+4*x^2)
-
Limit of (-4-7*x+2*x^2)/(4-13*x+3*x^2)
-
Limit of 5+3*n
-
Limit of (-12+x^2-4*x)/(48+x^2-14*x)
- Derivative of:
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2/x^3
- Integral of d{x}:
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2/x^3
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Identical expressions
- two /x^ three
- 2 divide by x cubed
- two divide by x to the power of three
- 2/x3
- 2/x³
- 2/x to the power of 3
- 2 divide by x^3
-
Similar expressions
- (-9+x^2)/(x^3-x^2-6*x)
- x^2/(x^3+3*x)
Limit of the function 2/x^3
The solution
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/2 \
lim |--|
x->oo| 3|
\x /
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right)$$
Limit(2/(x^3), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{3}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{3}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{3}\right)$$
=
$$2 \cdot 0^{3} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{3}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{3}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{3}\right)$$
=
$$2 \cdot 0^{3} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{2}{x^{3}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{2}{x^{3}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{3}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2}{x^{3}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{3}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{3}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{2}{x^{3}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{3}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2}{x^{3}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{3}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{3}}\right) = 0$$
More at x→-oo
The graph