Question

calcule lim x --> ∞ (x + 5) / 1 + ㏑x

Answer 1

Olá,

lim (x+5)/(1+ln(x)) = +∞/+∞
x → ∞

Utilizando a regra de L'Hôpital

Vamos derivar o numerador e o denominador:

d(x+5)/dx = 1
d(1+ln(x)) = 1/x

Logo,

lim (x+5)/(1+ln(x)) = lim (d(x+5)/dx)/(d(1+ln(x))/dx)
x → ∞

lim 1/(1/x) = (1/1)/(1/x) = 1/1·x/1 = x
x → ∞

Então,

lim (x+5)/(1+ln(x)) = x = +∞
x → ∞

Resposta:

lim (x+5)/(1+ln(x)) = +∞
x → ∞