Question

Lim (x^2-5x+6)/(x^2-12x+20) com x tendendo a 2

Answer 1

lim [x² - 5x + 6] / [x² - 12x + 20]
x -> 2

x² - 5x + 6 tirando as raízes => x₁ = 3, x₂ = 3 => fatoração => (x - 3).(x - 2)
x² - 12x + 20 tirando as raízes => x₁ = 10, x₂ = 2 => fatoração => (x - 10).(x - 2)

lim [(x - 3).(x - 2)] / [(x - 10) (x - 2)] ------ (x - 2) / (x - 2) = 1
x -> 2
lim (x - 3) / (x - 10)
x -> 2
lim (2 - 3) / (2 - 10) ---------  -1/-8 = 1/8
x -> 2