设 limx→af(x)=A,limx→ag(x)=Blim_{x \to a} f(x) = A, lim_{x \to a} g(x) = Blimx→af(x)=A,limx→ag(x)=B
线性运算
limx→a[kf(x)+lg(x)]=kA+lB lim_{x \to a} [kf(x) + lg(x)] = kA + lB limx→a[kf(x)+lg(x)]=kA+lB
乘法
limx→a[f(x)g(x)]=AB lim_{x \to a} [f(x)g(x)] = AB limx→a[f(x)g(x)]=AB
除法
limx→af(x)g(x)=AB lim_{x \to a} \dfrac{f(x)}{g(x)} = \dfrac{A}{B} limx→ag(x)f(x)=BA
乘方
limx→a[f(x)]km=Akm lim_{x \to a} [f(x)]^\frac{k}{m} = A^\frac{k}{m} limx→a[f(x)]mk=Amk
复合函数
已知 limx→x0g(x)=u0\lim_{x \to x_0} g(x) = u_0limx→x0g(x)=u0, limu→u0f(u)=A\lim_{u \to u_0} f(u) = Alimu→u0f(u)=A ⟹ limx→x0f(g(x))=A\implies \lim_{x \to x_0} f(g(x)) = A⟹limx→x0f(g(x))=A
