Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (3+2*n)/|-1+2*n|
-
Limit of (3+x^2-4*x)/(-9+x^2)
-
Limit of (x^2-3*x)/(-8+x^2)
-
Limit of (1+5*x)*(-1+5*x)
- Integral of d{x}:
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1/(x^2+2*x)
- Graphing y =:
- 1/(x^2+2*x)
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Identical expressions
- one /(x^ two + two *x)
- 1 divide by (x squared plus 2 multiply by x)
- one divide by (x to the power of two plus two multiply by x)
- 1/(x2+2*x)
- 1/x2+2*x
- 1/(x²+2*x)
- 1/(x to the power of 2+2*x)
- 1/(x^2+2x)
- 1/(x2+2x)
- 1/x2+2x
- 1/x^2+2x
- 1 divide by (x^2+2*x)
-
Similar expressions
- 1/(x^2-2*x)
Limit of the function 1/(x^2+2*x)
The solution
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1
lim --------
x->oo 2
x + 2*x
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x}$$
Limit(1/(x^2 + 2*x), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(1 + \frac{2}{x}\right)}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(1 + \frac{2}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{2 u + 1}\right)$$
=
$$\frac{0^{2}}{0 \cdot 2 + 1} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x} = 0$$
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(1 + \frac{2}{x}\right)}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(1 + \frac{2}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{2 u + 1}\right)$$
=
$$\frac{0^{2}}{0 \cdot 2 + 1} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x} = 0$$
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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \frac{1}{x^{2} + 2 x} = 0$$
$$\lim_{x \to 0^-} \frac{1}{x^{2} + 2 x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x^{2} + 2 x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x^{2} + 2 x} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{2} + 2 x} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x^{2} + 2 x} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{x^{2} + 2 x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x^{2} + 2 x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x^{2} + 2 x} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{2} + 2 x} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x^{2} + 2 x} = 0$$
More at x→-oo
The graph