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MAT 01353 – Ca´lculo e Geometria Anal´ıtica IA Limites infinitos e no infinito : Esquema Limites infinitos no infinito: -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 ↓ −∞ −∞← y x lim x→−∞ f(x) = −∞ -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4↑ +∞ −∞← y x lim x→−∞ f(x) = +∞ -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 ↓ −∞ → +∞ y x lim x→+∞ f(x) = −∞ -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4↑ +∞ → +∞ y x lim x→+∞ f(x) = +∞ Limites no infinito: -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 −∞← y x y = L e´ assint. horiz. L = −3 lim x→−∞ f(x) = L -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 → +∞ y x y = L e´ assint. horiz. L = 3 lim x→+∞ f(x) = L Limites infinitos: -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 ↑ +∞ 1 − x = 1 e´ assint. vert. y x lim x→1− f(x) = +∞ -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 ↓ −∞ 1 − x = 1 e´ assint. vert. y x lim x→1− f(x) = −∞ -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 ↑ +∞ 1 + x = 1 e´ assint. vert. y x lim x→1+ f(x) = +∞ -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 ↓ −∞ 1 + x = 1 e´ assint. vert. y x lim x→1+ f(x) = −∞
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