Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 10+x^2+3*x^3+8*x
-
Limit of (-2+sqrt(x))/(-4+x^2)
-
Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Derivative of:
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x^2-3*x
- Factor polynomial:
- x^2-3*x
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Identical expressions
- x^ two - three *x
- x squared minus 3 multiply by x
- x to the power of two minus three multiply by x
- x2-3*x
- x²-3*x
- x to the power of 2-3*x
- x^2-3x
- x2-3x
-
Similar expressions
- x^2+3*x
- (-3+x^2+2*x)/(2+x^2-3*x)
- (2+x^2-3*x)/(x-x^2)
- (8+x^2-6*x)/(-4+x^2-3*x)
- (1+x^2-3*x)/(-3-x^2+8*x)
Limit of the function x^2-3*x
The solution
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/ 2 \ lim \x - 3*x/ x->oo
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right)$$
Limit(x^2 - 3*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 3 u}{u^{2}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{3}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 3 u}{u^{2}}\right)$$
=
$$\frac{1 - 0}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{2} - 3 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} - 3 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} - 3 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} - 3 x\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} - 3 x\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} - 3 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} - 3 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} - 3 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} - 3 x\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} - 3 x\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} - 3 x\right) = \infty$$
More at x→-oo
The graph