Tip: Limits of Parametric Curves
Let be a parametric curve and let be an accumulation point of .
Then is the limit of for if and only if for each , there exists some such that for all
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Tip: Limits of Parametric Curves
Let γ:I⊆R→Rn be a parametric curve and let t0 be an accumulation point of I.
Then L∈Rn is the limit of γ for t→t0 if and only if for each ε>0, there exists some δ>0 such that for all t∈I
0<∣∣t−t0∣∣<δ⟹∣∣γ(t)−L∣∣<ε