Mister Exam
Autres calculateurs:
-
Comment utiliser ?
- Limite d'une fonction:
- Limite n2*(5/2+n/2)
-
Limite ((-4+3*x)/(2+3*x))^(2*x)
-
Limite (1+2*n)/|-1+2*n|
-
Limite (e^x-e^(-x))/(cos(x)*sin(x))
- Graphe de la fonction y =:
- 2+x
- Dérivée:
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2+x
- Intégrale d{x}:
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2+x
-
Expressions identiques
- two +x
- 2 plus x
- two plus x
-
Expressions similaires
- 2-x
Limite d'une fonction 2+x
Solution
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lim (2 + x) x->oo
$$\lim_{x \to \infty}\left(x + 2\right)$$
Limit(2 + x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x + 2\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(x + 2\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{2 u + 1}{u}\right)$$
=
$$\frac{0 \cdot 2 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x + 2\right) = \infty$$
$$\lim_{x \to \infty}\left(x + 2\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(x + 2\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{2 u + 1}{u}\right)$$
=
$$\frac{0 \cdot 2 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x + 2\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x + 2\right) = \infty$$
$$\lim_{x \to 0^-}\left(x + 2\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + 2\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x + 2\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + 2\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + 2\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x + 2\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + 2\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x + 2\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + 2\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + 2\right) = -\infty$$
More at x→-oo
Graphique