Mister Exam
Autres calculateurs:
-
Comment utiliser ?
- Limite d'une fonction:
-
Limite (3+2*x)/(1-5*x)
-
Limite (1-cos(2*x))*sin(x)/x
-
Limite (1-5^x)/(1-e^x)
-
Limite (1-2*cos(x))/sin(3*x)
- Intégrale d{x}:
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2/x^4
- Dérivée:
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2/x^4
- Graphe de la fonction y =:
- 2/x^4
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Expressions identiques
- two /x^ four
- 2 diviser par x à la puissance 4
- two diviser par x à la puissance four
- 2/x4
- 2/x⁴
- 2 divisé par x^4
-
Expressions similaires
- y*x^2/(x^4+y^4)
- (1-cos(x))^2/x^4
- x^2*y^2/(x^4+y^4)
Limite d'une fonction 2/x^4
Solution
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[src]
/2 \
lim |--|
x->oo| 4|
\x /
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right)$$
Limit(2/x^4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{4}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{4}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{4}\right)$$
=
$$2 \cdot 0^{4} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{4}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{4}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{4}\right)$$
=
$$2 \cdot 0^{4} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{2}{x^{4}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{2}{x^{4}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{4}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2}{x^{4}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{4}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{4}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{2}{x^{4}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{4}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2}{x^{4}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{4}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{4}}\right) = 0$$
More at x→-oo
Graphique