Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1/(-1+x)+2*x)^x
-
Limit of (4+2*n^3)/(5+n^2)
-
Limit of (2+n)^2/(n*(3+n))
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Limit of (-18+12*x+27*x^3)/(-30+2*x^3+5*x+8*x^2)
- Integral of d{x}:
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1/(x^2-2*x)
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Identical expressions
- one /(x^ two - two *x)
- 1 divide by (x squared minus 2 multiply by x)
- one divide by (x to the power of two minus 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)
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Similar expressions
- 1/(x^2+2*x)
- x^2/2-1/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
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(1 - \frac{2}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{1 - 2 u}\right)$$
=
$$\frac{0^{2}}{1 - 0} = 0$$
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
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(1 - \frac{2}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{1 - 2 u}\right)$$
=
$$\frac{0^{2}}{1 - 0} = 0$$
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
$$\lim_{x \to 1^-} \frac{1}{x^{2} - 2 x} = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{2} - 2 x} = -1$$
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
$$\lim_{x \to 1^-} \frac{1}{x^{2} - 2 x} = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x^{2} - 2 x} = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x^{2} - 2 x} = 0$$
More at x→-oo
The graph