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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)
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ᐥA function f:A→ℝ is differentiable at c if and only if
「(f(x)−f(c))/(x−c) Ƚx→c」
exists.
The value of the limit, called the derivative of f at c, is denoted by f(x)ᐁx「c」.ᐥ |