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Limit of the function/ x/y^2

Limit of the function x/y^2

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You have entered [src] 
     /x \
 lim |--|
y->oo| 2|
     \y /
lim⁡y→∞(xy2)\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right) 
Limit(x/y^2, y, oo, dir='-')
Detail solution
Let's take the limit
lim⁡y→∞(xy2)\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right)
Let's divide numerator and denominator by y^2:
lim⁡y→∞(xy2)\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right) =
lim⁡y→∞(x1y21)\lim_{y \to \infty}\left(\frac{x \frac{1}{y^{2}}}{1}\right)
Do Replacement
u=1yu = \frac{1}{y}
then
lim⁡y→∞(x1y21)=lim⁡u→0+(u2x)\lim_{y \to \infty}\left(\frac{x \frac{1}{y^{2}}}{1}\right) = \lim_{u \to 0^+}\left(u^{2} x\right)
=
02x=00^{2} x = 0

The final answer:
lim⁡y→∞(xy2)=0\lim_{y \to \infty}\left(\frac{x}{y^{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
Rapid solution [src] 
0
00
Expand and simplify
Other limits y→0, -oo, +oo, 1
lim⁡y→∞(xy2)=0\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right) = 0
lim⁡y→0−(xy2)=∞sign⁡(x)\lim_{y \to 0^-}\left(\frac{x}{y^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}
More at y→0 from the left
lim⁡y→0+(xy2)=∞sign⁡(x)\lim_{y \to 0^+}\left(\frac{x}{y^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}
More at y→0 from the right
lim⁡y→1−(xy2)=x\lim_{y \to 1^-}\left(\frac{x}{y^{2}}\right) = x
More at y→1 from the left
lim⁡y→1+(xy2)=x\lim_{y \to 1^+}\left(\frac{x}{y^{2}}\right) = x
More at y→1 from the right
lim⁡y→−∞(xy2)=0\lim_{y \to -\infty}\left(\frac{x}{y^{2}}\right) = 0
More at y→-oo
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