$A$ function $f$ from $R$ to $R$ is continuous at a point $a \in R$ if for each $\epsilon > 0$,there exists $\delta > 0$ such that:

  • A
    $|f(x) - f(a)| < \epsilon \implies |x - a| < \delta$
  • B
    $|f(x) - f(a)| > \epsilon \implies |x - a| > \delta$
  • C
    $|x - a| > \delta \implies |f(x) - f(a)| > \epsilon$
  • D
    $|x - a| < \delta \implies |f(x) - f(a)| < \epsilon$

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