Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
-
Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
-
Limit of (-14+x^2-5*x)/(-6+x+2*x^2)
-
Limit of (3+x^2+4*x)/(1+x^3)
- How do you in partial fractions?:
- 1/(x-x^2)
- Integral of d{x}:
-
1/(x-x^2)
- Graphing y =:
- 1/(x-x^2)
-
Identical expressions
- one /(x-x^ two)
- 1 divide by (x minus x squared )
- one divide by (x minus x to the power of two)
- 1/(x-x2)
- 1/x-x2
- 1/(x-x²)
- 1/(x-x to the power of 2)
- 1/x-x^2
- 1 divide by (x-x^2)
-
Similar expressions
- 2+1/x-x^2+x^3/(x^2+4*x)
- 1/(x+x^2)
Limit of the function 1/(x-x^2)
The solution
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1
lim ------
x->oo 2
x - x
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x}$$
Limit(1/(x - x^2), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(-1 + \frac{1}{x}\right)}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(-1 + \frac{1}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{u - 1}\right)$$
=
$$\frac{0^{2}}{-1} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x} = 0$$
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(-1 + \frac{1}{x}\right)}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x^{2} \left(-1 + \frac{1}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{u - 1}\right)$$
=
$$\frac{0^{2}}{-1} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x} = 0$$
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
$$\lim_{x \to \infty} \frac{1}{- x^{2} + x} = 0$$
$$\lim_{x \to 0^-} \frac{1}{- x^{2} + x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{- x^{2} + x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{- x^{2} + x} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{- x^{2} + x} = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{- x^{2} + x} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{- x^{2} + x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{- x^{2} + x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{- x^{2} + x} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{- x^{2} + x} = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{- x^{2} + x} = 0$$
More at x→-oo
The graph