Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-16+x^2-6*x)/(-2+x+x^2)
-
Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
-
Limit of (e^x-x-cos(x))/(-x+log(1+x))
-
Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
- (x+y)^2
- Integral of d{x}:
- (x+y)^2
- Canonical form:
- (x+y)^2
-
Identical expressions
- (x+y)^ two
- (x plus y) squared
- (x plus y) to the power of two
- (x+y)2
- x+y2
- (x+y)²
- (x+y) to the power of 2
- x+y^2
-
Similar expressions
- (x-y)^2
Limit of the function (x+y)^2
The solution
You have entered
[src]
2 lim (x + y) x->oo
$$\lim_{x \to \infty} \left(x + y\right)^{2}$$
Limit((x + y)^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \left(x + y\right)^{2}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \left(x + y\right)^{2}$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2 y}{x} + \frac{y^{2}}{x^{2}}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2 y}{x} + \frac{y^{2}}{x^{2}}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{u^{2} y^{2} + 2 u y + 1}{u^{2}}\right)$$
=
$$\frac{0^{2} y^{2} + 2 \cdot 0 y + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty} \left(x + y\right)^{2} = \infty$$
$$\lim_{x \to \infty} \left(x + y\right)^{2}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \left(x + y\right)^{2}$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2 y}{x} + \frac{y^{2}}{x^{2}}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2 y}{x} + \frac{y^{2}}{x^{2}}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{u^{2} y^{2} + 2 u y + 1}{u^{2}}\right)$$
=
$$\frac{0^{2} y^{2} + 2 \cdot 0 y + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty} \left(x + y\right)^{2} = \infty$$
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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \left(x + y\right)^{2} = \infty$$
$$\lim_{x \to 0^-} \left(x + y\right)^{2} = y^{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(x + y\right)^{2} = y^{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(x + y\right)^{2} = \left(y + 1\right)^{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(x + y\right)^{2} = \left(y + 1\right)^{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(x + y\right)^{2} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \left(x + y\right)^{2} = y^{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(x + y\right)^{2} = y^{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(x + y\right)^{2} = \left(y + 1\right)^{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(x + y\right)^{2} = \left(y + 1\right)^{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(x + y\right)^{2} = \infty$$
More at x→-oo