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

Limit of the function 2/x^2

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     /2 \
 lim |--|
x->oo| 2|
     \x /
lim⁡x→∞(2x2)\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right) 
Limit(2/x^2, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(2x2)\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right)
Let's divide numerator and denominator by x^2:
lim⁡x→∞(2x2)\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right) =
lim⁡x→∞(21x21)\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{2}}}{1}\right)
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞(21x21)=lim⁡u→0+(2u2)\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{2}\right)
=
2⋅02=02 \cdot 0^{2} = 0

The final answer:
lim⁡x→∞(2x2)=0\lim_{x \to \infty}\left(\frac{2}{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
02468-8-6-4-2-10100200
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(2x2)=0\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right) = 0
lim⁡x→0−(2x2)=∞\lim_{x \to 0^-}\left(\frac{2}{x^{2}}\right) = \infty
More at x→0 from the left
lim⁡x→0+(2x2)=∞\lim_{x \to 0^+}\left(\frac{2}{x^{2}}\right) = \infty
More at x→0 from the right
lim⁡x→1−(2x2)=2\lim_{x \to 1^-}\left(\frac{2}{x^{2}}\right) = 2
More at x→1 from the left
lim⁡x→1+(2x2)=2\lim_{x \to 1^+}\left(\frac{2}{x^{2}}\right) = 2
More at x→1 from the right
lim⁡x→−∞(2x2)=0\lim_{x \to -\infty}\left(\frac{2}{x^{2}}\right) = 0
More at x→-oo
The graph
Limit of the function 2/x^2
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