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