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Limit of the function/ x^(-2)

Limit of the function x^(-2)

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     1 
 lim --
x->oo 2
     x

\lim_{x \to \infty} \frac{1}{x^{2}}

Limit(x^(-2), x, oo, dir='-')

Detail solution

Let's take the limit

\lim_{x \to \infty} \frac{1}{x^{2}}

Let's divide numerator and denominator by x^2:

\lim_{x \to \infty} \frac{1}{x^{2}}

\lim_{x \to \infty}\left(\frac{1}{x^{2}}\right)

Do Replacement

u = \frac{1}{x}

then

\lim_{x \to \infty}\left(\frac{1}{x^{2}}\right) = \lim_{u \to 0^+} u^{2}

0^{2} = 0

The final answer:

\lim_{x \to \infty} \frac{1}{x^{2}} = 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} \frac{1}{x^{2}} = 0

\lim_{x \to 0^-} \frac{1}{x^{2}} = \infty

\lim_{x \to 0^+} \frac{1}{x^{2}} = \infty

\lim_{x \to 1^-} \frac{1}{x^{2}} = 1

\lim_{x \to 1^+} \frac{1}{x^{2}} = 1

\lim_{x \to -\infty} \frac{1}{x^{2}} = 0

The graph