Mister Exam
Autres calculateurs:
-
Comment utiliser ?
- Limite d'une fonction:
-
Limite ((3+x)^2+(3-x)^2)/((3-x)^2-(3+x)^2)
-
Limite ((3+2*x)/(7+5*x))^(1+x)
-
Limite ((1+2*x)/(-1+x))^(4*x)
-
Limite (-6+x+x^2)/(3+x)
- Dérivée:
-
3/x
- Intégrale d{x}:
-
3/x
- Graphe de la fonction y =:
- 3/x
-
Expressions identiques
- three /x
- 3 diviser par x
- three diviser par x
- 3 divisé par x
Limite d'une fonction 3/x
Solution
You have entered
[src]
/3\ lim |-| x->oo\x/
$$\lim_{x \to \infty}\left(\frac{3}{x}\right)$$
Limit(3/x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{3}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{3}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{3 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{3 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(3 u\right)$$
=
$$0 \cdot 3 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{3}{x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{3}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{3}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{3 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{3 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(3 u\right)$$
=
$$0 \cdot 3 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{3}{x}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{3}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{3}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3}{x}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3}{x}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{3}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3}{x}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3}{x}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3}{x}\right) = 0$$
More at x→-oo
Graphique