定理imf(x)=Aimf(x)=lmf(x)=A x→)x limf(x)=A分V0,3X>0,当x<-X有 f(x)-4<6 e lim f(x)=AVe>0,3X>0,当x>Y有 x→)+00 (x)-4<6 定理 limf(x)=Ae lim f(x)=lim f(x)=A →)+0定理 ( ) ( ) ( ) 0 0 0 lim lim lim . x x x x x x f x A f x f x A → → → − + = ⇔ = = lim ( ) 0, 0, x f x A ε X x X →−∞ = ⇔ ∀ > ∃ > 当 有 < − f x( ) − A < ε. lim ( ) 0, 0, x f x A ε X x X →+∞ = ⇔ ∀ > ∃ > 当 有 > f x( ) − A < ε. 定理 lim ( ) lim ( ) lim ( ) . x x x f x A f x f x A →∞ →−∞ →+∞ = ⇔ = =