Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
- Limit of (1+2*x/3)^(3251035981008077*x/140737488355328)
-
Limit of 4+((3+x)/(5+x))^x
-
Limit of (-343+x^3)/(-7+x)
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Limit of (-2+x^2-x)/(x^2-2*x)
- Derivative of:
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2-x-x^3
- Graphing y =:
- 2-x-x^3
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Identical expressions
- two -x-x^ three
- 2 minus x minus x cubed
- two minus x minus x to the power of three
- 2-x-x3
- 2-x-x³
- 2-x-x to the power of 3
-
Similar expressions
- 2+x-x^3
- 2-x+x^3
Limit of the function 2-x-x^3
The solution
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/ 3\ lim \2 - x - x / x->-oo
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right)$$
Limit(2 - x - x^3, x, -oo)
Detail solution
Let's take the limit
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{-1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{-1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{2 u^{3} - u^{2} - 1}{u^{3}}\right)$$
=
$$\frac{-1 - 0^{2} + 2 \cdot 0^{3}}{0} = \infty$$
The final answer:
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right) = \infty$$
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{-1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{-1 - \frac{1}{x^{2}} + \frac{2}{x^{3}}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{2 u^{3} - u^{2} - 1}{u^{3}}\right)$$
=
$$\frac{-1 - 0^{2} + 2 \cdot 0^{3}}{0} = \infty$$
The final answer:
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right) = \infty$$
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
$$\lim_{x \to -\infty}\left(- x^{3} + \left(2 - x\right)\right) = \infty$$
$$\lim_{x \to \infty}\left(- x^{3} + \left(2 - x\right)\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x^{3} + \left(2 - x\right)\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{3} + \left(2 - x\right)\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{3} + \left(2 - x\right)\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{3} + \left(2 - x\right)\right) = 0$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(- x^{3} + \left(2 - x\right)\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x^{3} + \left(2 - x\right)\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{3} + \left(2 - x\right)\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{3} + \left(2 - x\right)\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{3} + \left(2 - x\right)\right) = 0$$
More at x→1 from the right
The graph