Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of exp(2*x)
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Limit of 2*x^2
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Limit of e^(-x)/x
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Limit of x^3-2*x^2
- Factor polynomial:
- x^3-2*x^2
- Derivative of:
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x^3-2*x^2
- Graphing y =:
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x^3-2*x^2
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Identical expressions
- x^ three - two *x^ two
- x cubed minus 2 multiply by x squared
- x to the power of three minus two multiply by x to the power of two
- x3-2*x2
- x³-2*x²
- x to the power of 3-2*x to the power of 2
- x^3-2x^2
- x3-2x2
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Similar expressions
- x^3+2*x^2
Limit of the function x^3-2*x^2
The solution
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/ 3 2\ lim \x - 2*x / x->oo
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right)$$
Limit(x^3 - 2*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{2}{x}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{2}{x}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 2 u}{u^{3}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{2}{x}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{2}{x}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 2 u}{u^{3}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{3} - 2 x^{2}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{3} - 2 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} - 2 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{3} - 2 x^{2}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} - 2 x^{2}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} - 2 x^{2}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{3} - 2 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} - 2 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{3} - 2 x^{2}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} - 2 x^{2}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} - 2 x^{2}\right) = -\infty$$
More at x→-oo
The graph