Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of 10+x^2+3*x^3+8*x
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Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
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Limit of (-4+x^2)/(-3+sqrt(1-4*x))
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Limit of ((1+x)/(-2+x))^(3+x)
- Integral of d{x}:
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x^3/3
- Derivative of:
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x^3/3
- Graphing y =:
- x^3/3
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Identical expressions
- x^ three / three
- x cubed divide by 3
- x to the power of three divide by three
- x3/3
- x³/3
- x to the power of 3/3
- x^3 divide by 3
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Similar expressions
- (x-x^3)/(3*x^2)
- (1+x)^3/(3*x^3)
- -11/3+x^2+3*x-x^3/3
- (x+4*x^3)/(3-x+2*x^2)
- (x-x^3)/(31+2*x^2)
Limit of the function x^3/3
The solution
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/ 3\
|x |
lim |--|
x->oo\3 /
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right)$$
Limit(x^3/3, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{3 \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{3 \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{1}{3 u^{3}}\right)$$
=
$$\frac{1}{0 \cdot 3} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{3 \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{3 \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{1}{3 u^{3}}\right)$$
=
$$\frac{1}{0 \cdot 3} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{x^{3}}{3}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x^{3}}{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{3}}{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{3}}{3}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{3}}{3}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{3}}{3}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x^{3}}{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{3}}{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{3}}{3}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{3}}{3}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{3}}{3}\right) = -\infty$$
More at x→-oo
The graph