Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 7^(1/(-3+x))
-
Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
-
Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
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Limit of (-6-x^2-3*x+4*x^3)/(3-x^2+2*x^3)
- Derivative of:
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x^3-5*x
- Graphing y =:
- x^3-5*x
- Factor polynomial:
- x^3-5*x
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Identical expressions
- x^ three - five *x
- x cubed minus 5 multiply by x
- x to the power of three minus five multiply by x
- x3-5*x
- x³-5*x
- x to the power of 3-5*x
- x^3-5x
- x3-5x
-
Similar expressions
- (x+e^x)/(x^3-5*x)
- 3-x^3-5*x^4+2*x^2+10*x
- x^3+5*x
Limit of the function x^3-5*x
The solution
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/ 3 \ lim \x - 5*x/ x->oo
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right)$$
Limit(x^3 - 5*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x^{2}}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x^{2}}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 5 u^{2}}{u^{3}}\right)$$
=
$$\frac{1 - 5 \cdot 0^{2}}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x^{2}}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x^{2}}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - 5 u^{2}}{u^{3}}\right)$$
=
$$\frac{1 - 5 \cdot 0^{2}}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{3} - 5 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{3} - 5 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} - 5 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{3} - 5 x\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} - 5 x\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} - 5 x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{3} - 5 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} - 5 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{3} - 5 x\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} - 5 x\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} - 5 x\right) = -\infty$$
More at x→-oo
The graph