Pillow English Listening

› ε-δ definition
9732#39169 SBLNGS CHLDRN OPN

• 513 Rules
ᐥSuppose that ｢f(x)︱x￫a｣=L and ｢g(x)︱x￫a｣=M. Then the following rules apply. ❶ sum rule ｢f(x)+g(x)︱x￫a｣ = L+M ❷ product rule ｢f(x)·g(x)︱x￫a｣ = L·M ❸ quotient rule ｢f(x)/g(x)︱x￫a｣ = L/M provided that M≠0ᐥ Proof of ❶ ∀ε>0 ∃δ>0 such that 0<|x−a|<δ ⇒ ∣f(x)−L ...
9732#9735 SBLNGS CHLDRN 9735

• 522 Continuous
f is continuous at c if and only if for every ε>0 there exists δ>0 such that |x−c|<δ ⇒ |f(x)−f(c)|<ε. ┆｢f(x) Ƚx￫c｣ = f(c)┆
9732#9756 SBLNGS CHLDRN 9756