Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-5+7*n)/(2+n)
-
Limit of (-64+4^x)/(-3+x)
-
Limit of (-7+3*x^2+5*x)/(1+x+3*x^2)
-
Limit of (-2+2*x^3+7*x)/(-4-x+3*x^3)
- The double integral of:
- x/y^2
- x/y^2
-
Identical expressions
- x/y^ two
- x divide by y squared
- x divide by y to the power of two
- x/y2
- x/y²
- x/y to the power of 2
- x divide by y^2
Limit of the function x/y^2
The solution
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[src]
/x \
lim |--|
y->oo| 2|
\y /
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right)$$
Limit(x/y^2, y, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right)$$
Let's divide numerator and denominator by y^2:
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right)$$ =
$$\lim_{y \to \infty}\left(\frac{x \frac{1}{y^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{y}$$
then
$$\lim_{y \to \infty}\left(\frac{x \frac{1}{y^{2}}}{1}\right) = \lim_{u \to 0^+}\left(u^{2} x\right)$$
=
$$0^{2} x = 0$$
The final answer:
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right) = 0$$
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right)$$
Let's divide numerator and denominator by y^2:
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right)$$ =
$$\lim_{y \to \infty}\left(\frac{x \frac{1}{y^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{y}$$
then
$$\lim_{y \to \infty}\left(\frac{x \frac{1}{y^{2}}}{1}\right) = \lim_{u \to 0^+}\left(u^{2} x\right)$$
=
$$0^{2} x = 0$$
The final answer:
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right) = 0$$
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
Other limits y→0, -oo, +oo, 1
$$\lim_{y \to \infty}\left(\frac{x}{y^{2}}\right) = 0$$
$$\lim_{y \to 0^-}\left(\frac{x}{y^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}$$
More at y→0 from the left
$$\lim_{y \to 0^+}\left(\frac{x}{y^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}$$
More at y→0 from the right
$$\lim_{y \to 1^-}\left(\frac{x}{y^{2}}\right) = x$$
More at y→1 from the left
$$\lim_{y \to 1^+}\left(\frac{x}{y^{2}}\right) = x$$
More at y→1 from the right
$$\lim_{y \to -\infty}\left(\frac{x}{y^{2}}\right) = 0$$
More at y→-oo
$$\lim_{y \to 0^-}\left(\frac{x}{y^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}$$
More at y→0 from the left
$$\lim_{y \to 0^+}\left(\frac{x}{y^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}$$
More at y→0 from the right
$$\lim_{y \to 1^-}\left(\frac{x}{y^{2}}\right) = x$$
More at y→1 from the left
$$\lim_{y \to 1^+}\left(\frac{x}{y^{2}}\right) = x$$
More at y→1 from the right
$$\lim_{y \to -\infty}\left(\frac{x}{y^{2}}\right) = 0$$
More at y→-oo