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Limit of the function/ 2/x^3

Limit of the function 2/x^3

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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

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]

0

Expand and simplify

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

\lim_{x \to 0^+}\left(\frac{2}{x^{3}}\right) = \infty

\lim_{x \to 1^-}\left(\frac{2}{x^{3}}\right) = 2

\lim_{x \to 1^+}\left(\frac{2}{x^{3}}\right) = 2

\lim_{x \to -\infty}\left(\frac{2}{x^{3}}\right) = 0

The graph