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