Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((-4+3*x)/(2+3*x))^(2*x)
-
Limit of (3+x^2-x)/(-3+3*x+5*x^2)
-
Limit of (-1+x^2)/(-2+x+x^2)
-
Limit of (sqrt(5+x)-sqrt(10))/(-15+x^2-2*x)
- Graphing y =:
- x-x^2
- Factor polynomial:
- x-x^2
- Derivative of:
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x-x^2
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Identical expressions
- x-x^ two
- x minus x squared
- x minus x to the power of two
- x-x2
- x-x²
- x-x to the power of 2
-
Similar expressions
- x-x^2*atan(1/x)
- tan(5*x)/(x-x^2)
- x+x^2
- (2+x^2-3*x)/(x-x^2)
- (-x-x^2)/(2+2*x^2+3*x)
Limit of the function x-x^2
The solution
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/ 2\ lim \x - x / x->-oo
$$\lim_{x \to -\infty}\left(- x^{2} + x\right)$$
Limit(x - x^2, x, -oo)
Detail solution
Let's take the limit
$$\lim_{x \to -\infty}\left(- x^{2} + x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to -\infty}\left(- x^{2} + x\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{u - 1}{u^{2}}\right)$$
=
$$\frac{-1}{0} = -\infty$$
The final answer:
$$\lim_{x \to -\infty}\left(- x^{2} + x\right) = -\infty$$
$$\lim_{x \to -\infty}\left(- x^{2} + x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to -\infty}\left(- x^{2} + x\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{u - 1}{u^{2}}\right)$$
=
$$\frac{-1}{0} = -\infty$$
The final answer:
$$\lim_{x \to -\infty}\left(- x^{2} + x\right) = -\infty$$
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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -\infty}\left(- x^{2} + x\right) = -\infty$$
$$\lim_{x \to \infty}\left(- x^{2} + x\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x^{2} + x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2} + x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + x\right) = 0$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(- x^{2} + x\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x^{2} + x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2} + x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + x\right) = 0$$
More at x→1 from the right
The graph