Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (4+x^2)/(-6+2*x)
-
Limit of ((1+x)/(1+2*x))^x
-
Limit of (n/(1+n))^(5+3*n)
-
Limit of (9^x-8^x)/asin(3*x)
- The double integral of:
- (x-y)/(x+y)^3
- Integral of d{x}:
- (x-y)/(x+y)^3
-
Identical expressions
- (x-y)/(x+y)^ three
- (x minus y) divide by (x plus y) cubed
- (x minus y) divide by (x plus y) to the power of three
- (x-y)/(x+y)3
- x-y/x+y3
- (x-y)/(x+y)³
- (x-y)/(x+y) to the power of 3
- x-y/x+y^3
- (x-y) divide by (x+y)^3
-
Similar expressions
- (x+y)/(x+y)^3
- (x-y)/(x-y)^3
Limit of the function (x-y)/(x+y)^3
The solution
You have entered
[src]
/ x - y \
lim |--------|
x->0+| 3|
\(x + y) /
$$\lim_{x \to 0^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right)$$
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
One‐sided limits
[src]
/ x - y \
lim |--------|
x->0+| 3|
\(x + y) /
$$\lim_{x \to 0^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right)$$
-1 --- 2 y
$$- \frac{1}{y^{2}}$$
/ x - y \
lim |--------|
x->0-| 3|
\(x + y) /
$$\lim_{x \to 0^-}\left(\frac{x - y}{\left(x + y\right)^{3}}\right)$$
-1 --- 2 y
$$- \frac{1}{y^{2}}$$
-1/y^2
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{1}{y^{2}}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{1}{y^{2}}$$
$$\lim_{x \to \infty}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{y - 1}{y^{3} + 3 y^{2} + 3 y + 1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{y - 1}{y^{3} + 3 y^{2} + 3 y + 1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{1}{y^{2}}$$
$$\lim_{x \to \infty}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{y - 1}{y^{3} + 3 y^{2} + 3 y + 1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = - \frac{y - 1}{y^{3} + 3 y^{2} + 3 y + 1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x - y}{\left(x + y\right)^{3}}\right) = 0$$
More at x→-oo