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Limit of the function/ x^9

Limit of the function x^9

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The solution

You have entered [src] 
      9
 lim x 
x->oo
lim⁡x→∞x9\lim_{x \to \infty} x^{9} 
Limit(x^9, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞x9\lim_{x \to \infty} x^{9}
Let's divide numerator and denominator by x^9:
lim⁡x→∞x9\lim_{x \to \infty} x^{9} =
lim⁡x→∞11x9\lim_{x \to \infty} \frac{1}{\frac{1}{x^{9}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞11x9=lim⁡u→0+1u9\lim_{x \to \infty} \frac{1}{\frac{1}{x^{9}}} = \lim_{u \to 0^+} \frac{1}{u^{9}}
=
10=∞\frac{1}{0} = \infty

The final answer:
lim⁡x→∞x9=∞\lim_{x \to \infty} x^{9} = \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
02468-8-6-4-2-1010-20000000002000000000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→∞x9=∞\lim_{x \to \infty} x^{9} = \infty
lim⁡x→0−x9=0\lim_{x \to 0^-} x^{9} = 0
More at x→0 from the left
lim⁡x→0+x9=0\lim_{x \to 0^+} x^{9} = 0
More at x→0 from the right
lim⁡x→1−x9=1\lim_{x \to 1^-} x^{9} = 1
More at x→1 from the left
lim⁡x→1+x9=1\lim_{x \to 1^+} x^{9} = 1
More at x→1 from the right
lim⁡x→−∞x9=−∞\lim_{x \to -\infty} x^{9} = -\infty
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
The graph
Limit of the function x^9
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