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Limit of the function/ x^6

Limit of the function x^6

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      6
 lim x 
x->oo

\lim_{x \to \infty} x^{6}

Limit(x^6, x, oo, dir='-')

Detail solution

Let's take the limit

\lim_{x \to \infty} x^{6}

Let's divide numerator and denominator by x^6:

\lim_{x \to \infty} x^{6}

\lim_{x \to \infty} \frac{1}{\frac{1}{x^{6}}}

Do Replacement

u = \frac{1}{x}

then

\lim_{x \to \infty} \frac{1}{\frac{1}{x^{6}}} = \lim_{u \to 0^+} \frac{1}{u^{6}}

\frac{1}{0} = \infty

The final answer:

\lim_{x \to \infty} x^{6} = \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 x→0, -oo, +oo, 1

\lim_{x \to \infty} x^{6} = \infty

\lim_{x \to 0^-} x^{6} = 0

\lim_{x \to 0^+} x^{6} = 0

\lim_{x \to 1^-} x^{6} = 1

\lim_{x \to 1^+} x^{6} = 1

\lim_{x \to -\infty} x^{6} = \infty

The graph