Mister Exam

Other calculators:

n^3
Limit of the function/ n^3

Limit of the function n^3

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

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

The final answer:
$$\lim_{n \to \infty} n^{3} = \infty$$
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
Plot the graph
Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty} n^{3} = \infty$$
$$\lim_{n \to 0^-} n^{3} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} n^{3} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} n^{3} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} n^{3} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} n^{3} = -\infty$$
More at n→-oo
The graph
Limit of the function n^3
    © Mister Exam – Calculator