Limites e limites fundamentais

Prévia do material em texto

Tabela de Limites
lim f(x) lim g(x) h(x) limh(x) Simbolicamente
±∞ ±∞ f(x) + g(x) ±∞ ±∞±∞→ ±∞
+∞ +∞ f(x)− g(x) ? (+∞)− (+∞)
+∞ k f(x) + g(x) +∞ +∞+ k → +∞
−∞ k f(x) + g(x) −∞ −∞+ k → −∞
+∞ +∞ f(x) · g(x) +∞ (+∞) · (+∞)→ +∞
+∞ −∞ f(x) · g(x) −∞ (+∞) · (−∞)→ −∞
+∞ k > 0 f(x) · g(x) +∞ +∞ · k → +∞, k > 0
+∞ k < 0 f(x) · g(x) −∞ +∞ · k → −∞, k < 0
±∞ 0 f(x) · g(x) ? ±∞ · 0
k ±∞ f(x)/g(x) 0 k/±∞→ 0
±∞ ±∞ f(x)/g(x) ? ±∞/±∞
k > 0 0+ f(x)/g(x) +∞ k/0+ → +∞, k > 0
+∞ 0+ f(x)/g(x) +∞ +∞/0+ → +∞
k > 0 0− f(x)/g(x) −∞ k/0− → −∞, k > 0
+∞ 0− f(x)/g(x) −∞ −∞/0− → −∞
0 0 f(x)/g(x) ? 0/0
Limites Fundamentais
lim
x→0
senx
x
= 1
lim
x→±∞
(
1 +
1
x
)x
= e
lim
x→0
ax − 1
x
= ln a
1