函数的极限

2025-09-09 00:00

导入

y=x2y=x^2在(1,1)处的切线的斜率

k(x1)=x2−1x−1=(x−1)(x+1)x−1=x+1 k(x_1) = \frac{x^2-1}{x-1} = \frac{(x-1)(x+1)}{x-1} = x+1

定义

函数极限的定义 ε−δ\varepsilon - \delta 语言

∀ε>0\forall \varepsilon >0,∃δ>0,x∈(a−δ,a+δ)⇒∣f(x)−b∣<ε\exist \delta > 0,x \in (a-\delta,a+\delta) \Rightarrow \left| f(x)-b \right| < \varepsilon

lim⁡x→af(x)=b\lim \limits_{x \to a} f(x) = b

hugo