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Defining Limits and Using Limit Notation

AP Calculus AB· difficulty 1/5

The statement "lim⁡x→af(x)=L\lim_{x \to a} f(x) = L" means

  • A

    f(x)f(x) can be made arbitrarily close to LL by taking xx sufficiently close to aa (but x≠ax \ne a)

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  • B

    f(a)=Lf(a) = L

  • C

    LL is the maximum value of ff near aa

  • D

    ff takes the value LL on some interval around aa

Explanation

The informal ϵ\epsilon-δ\delta idea: arbitrarily close to LL for xx near aa (excluding aa itself).

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