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n^3
Limit of the function/ n^3

Limit of the function n^3

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The solution

You have entered [src] 
      3
 lim n 
n->oo
lim⁡n→∞n3\lim_{n \to \infty} n^{3} 
Limit(n^3, n, oo, dir='-')
Detail solution
Let's take the limit
lim⁡n→∞n3\lim_{n \to \infty} n^{3}
Let's divide numerator and denominator by n^3:
lim⁡n→∞n3\lim_{n \to \infty} n^{3} =
lim⁡n→∞11n3\lim_{n \to \infty} \frac{1}{\frac{1}{n^{3}}}
Do Replacement
u=1nu = \frac{1}{n}
then
lim⁡n→∞11n3=lim⁡u→0+1u3\lim_{n \to \infty} \frac{1}{\frac{1}{n^{3}}} = \lim_{u \to 0^+} \frac{1}{u^{3}}
=
10=∞\frac{1}{0} = \infty

The final answer:
lim⁡n→∞n3=∞\lim_{n \to \infty} n^{3} = \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
02468-8-6-4-2-1010-20002000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits n→0, -oo, +oo, 1
lim⁡n→∞n3=∞\lim_{n \to \infty} n^{3} = \infty
lim⁡n→0−n3=0\lim_{n \to 0^-} n^{3} = 0
More at n→0 from the left
lim⁡n→0+n3=0\lim_{n \to 0^+} n^{3} = 0
More at n→0 from the right
lim⁡n→1−n3=1\lim_{n \to 1^-} n^{3} = 1
More at n→1 from the left
lim⁡n→1+n3=1\lim_{n \to 1^+} n^{3} = 1
More at n→1 from the right
lim⁡n→−∞n3=−∞\lim_{n \to -\infty} n^{3} = -\infty
More at n→-oo
The graph
Limit of the function n^3
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