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 (-2+sqrt(x))/(-4+x^2)
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Graphing y =:
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x^(-3)
- Derivative of:
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x^(-3)
- Integral of d{x}:
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x^(-3)
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Identical expressions
- x^(- three)
- x to the power of ( minus 3)
- x to the power of ( minus three)
- x(-3)
- x-3
- x^-3
-
Similar expressions
- cot(4+2*x)^(-3)
- (1+4/(1+4*x))^(-3+2*x)
- (1+4*x)^((-3+x)/x)
- (1+2/x)^(-3*x)
- x^(3)
Limit of the function x^(-3)
The solution
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1
lim --
x->oo 3
x
$$\lim_{x \to \infty} \frac{1}{x^{3}}$$
Limit(x^(-3), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \frac{1}{x^{3}}$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty} \frac{1}{x^{3}}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x^{3}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x^{3}}\right) = \lim_{u \to 0^+} u^{3}$$
=
$$0^{3} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{x^{3}} = 0$$
$$\lim_{x \to \infty} \frac{1}{x^{3}}$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty} \frac{1}{x^{3}}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x^{3}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x^{3}}\right) = \lim_{u \to 0^+} u^{3}$$
=
$$0^{3} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{x^{3}} = 0$$
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
$$\lim_{x \to \infty} \frac{1}{x^{3}} = 0$$
$$\lim_{x \to 0^-} \frac{1}{x^{3}} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x^{3}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x^{3}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{3}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x^{3}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{x^{3}} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x^{3}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x^{3}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{3}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x^{3}} = 0$$
More at x→-oo
The graph