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x^8
Limit of the function/ x^8

Limit of the function x^8

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The solution

You have entered [src] 
      8
 lim x 
x->oo
$$\lim_{x \to \infty} x^{8}$$ 
Limit(x^8, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} x^{8}$$
Let's divide numerator and denominator by x^8:
$$\lim_{x \to \infty} x^{8}$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{8}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{8}}} = \lim_{u \to 0^+} \frac{1}{u^{8}}$$
=
$$\frac{1}{0} = \infty$$

The final answer:
$$\lim_{x \to \infty} x^{8} = \infty$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} x^{8} = \infty$$
$$\lim_{x \to 0^-} x^{8} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{8} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{8} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{8} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{8} = \infty$$
More at x→-oo
Rapid solution [src] 
oo
$$\infty$$
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The graph
Limit of the function x^8
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