Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of x^3-3*x^2
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Limit of sign(x)
-
Limit of -sinh(x)+cosh(x)
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Limit of 3+3*n^2+5*n-32*n^3/5
- Graphing y =:
- x^3-3*x^2
- Derivative of:
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x^3-3*x^2
- Integral of d{x}:
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x^3-3*x^2
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Identical expressions
- x^ three - three *x^ two
- x cubed minus 3 multiply by x squared
- x to the power of three minus three multiply by x to the power of two
- x3-3*x2
- x³-3*x²
- x to the power of 3-3*x to the power of 2
- x^3-3x^2
- x3-3x2
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Similar expressions
- x^3+3*x^2
Limit of the function x^3-3*x^2
The solution
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/ 3 2\ lim \x - 3*x / x->oo
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right)$$
Limit(x^3 - 3*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 3 u}{u^{3}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 3 u}{u^{3}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{3} - 3 x^{2}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{3} - 3 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} - 3 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{3} - 3 x^{2}\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} - 3 x^{2}\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} - 3 x^{2}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{3} - 3 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} - 3 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{3} - 3 x^{2}\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} - 3 x^{2}\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} - 3 x^{2}\right) = -\infty$$
More at x→-oo
The graph