Mister Exam

Other calculators:

Limit of the function/ (x-y)/(x+y)^3

Limit of the function (x-y)/(x+y)^3

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     / x - y  \
 lim |--------|
x->0+|       3|
     \(x + y) /
lim⁡x→0+(x−y(x+y)3)\lim_{x \to 0^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) 
Limit((x - y)/(x + y)^3, x, 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] 
-1 
---
  2
 y
−1y2- \frac{1}{y^{2}}
Expand and simplify
One‐sided limits [src] 
     / x - y  \
 lim |--------|
x->0+|       3|
     \(x + y) /
lim⁡x→0+(x−y(x+y)3)\lim_{x \to 0^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) 
-1 
---
  2
 y
−1y2- \frac{1}{y^{2}} 
     / x - y  \
 lim |--------|
x->0-|       3|
     \(x + y) /
lim⁡x→0−(x−y(x+y)3)\lim_{x \to 0^-}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) 
-1 
---
  2
 y
−1y2- \frac{1}{y^{2}} 
-1/y^2
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(x−y(x+y)3)=−1y2\lim_{x \to 0^-}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{1}{y^{2}}
More at x→0 from the left
lim⁡x→0+(x−y(x+y)3)=−1y2\lim_{x \to 0^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{1}{y^{2}}
lim⁡x→∞(x−y(x+y)3)=0\lim_{x \to \infty}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = 0
More at x→oo
lim⁡x→1−(x−y(x+y)3)=−y−1y3+3y2+3y+1\lim_{x \to 1^-}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{y - 1}{y^{3} + 3 y^{2} + 3 y + 1}
More at x→1 from the left
lim⁡x→1+(x−y(x+y)3)=−y−1y3+3y2+3y+1\lim_{x \to 1^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{y - 1}{y^{3} + 3 y^{2} + 3 y + 1}
More at x→1 from the right
lim⁡x→−∞(x−y(x+y)3)=0\lim_{x \to -\infty}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = 0
More at x→-oo
    © Mister Exam – Calculator