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8/x^2
Limit of the function/ 8/x^2

Limit of the function 8/x^2

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     /8 \
 lim |--|
x->oo| 2|
     \x /
lim⁡x→∞(8x2)\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right) 
Limit(8/x^2, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(8x2)\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right)
Let's divide numerator and denominator by x^2:
lim⁡x→∞(8x2)\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right) =
lim⁡x→∞(81x21)\lim_{x \to \infty}\left(\frac{8 \frac{1}{x^{2}}}{1}\right)
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞(81x21)=lim⁡u→0+(8u2)\lim_{x \to \infty}\left(\frac{8 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(8 u^{2}\right)
=
8⋅02=08 \cdot 0^{2} = 0

The final answer:
lim⁡x→∞(8x2)=0\lim_{x \to \infty}\left(\frac{8}{x^{2}}\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
02468-8-6-4-2-101001000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(8x2)=0\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right) = 0
lim⁡x→0−(8x2)=∞\lim_{x \to 0^-}\left(\frac{8}{x^{2}}\right) = \infty
More at x→0 from the left
lim⁡x→0+(8x2)=∞\lim_{x \to 0^+}\left(\frac{8}{x^{2}}\right) = \infty
More at x→0 from the right
lim⁡x→1−(8x2)=8\lim_{x \to 1^-}\left(\frac{8}{x^{2}}\right) = 8
More at x→1 from the left
lim⁡x→1+(8x2)=8\lim_{x \to 1^+}\left(\frac{8}{x^{2}}\right) = 8
More at x→1 from the right
lim⁡x→−∞(8x2)=0\lim_{x \to -\infty}\left(\frac{8}{x^{2}}\right) = 0
More at x→-oo
Rapid solution [src] 
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The graph
Limit of the function 8/x^2
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