ContinuityThe limit of a function fff at x0x_0x0 is LLL iff limx→x0f(x)=L{\lim\limits_{x \to x_0}} f (x) = Lx→x0limf(x)=L iff ∀ϵ>0,∃δ>0:∀x:0<∣x−x0∣<δ→∣f(x)−L∣<ϵ\forall \epsilon > 0, \exists \delta >0 : \forall x : 0 < |x - x_0| < \delta \to |f(x) - L| < \epsilon∀ϵ>0,∃δ>0:∀x:0<∣x−x0∣<δ→∣f(x)−L∣<ϵ fff does not need to exist at x0x_0x0 to define the limit. However, for the function to be continuous, the limx→x0f(x)=f(x0)\lim\limits_{x \to x_0} f(x) = f(x_0)x→x0limf(x)=f(x0).Backlinks (1)230307Comments (0)
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