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Squeeze Theorem

AP Calculus AB· difficulty 3/5

If −x2≤f(x)≤x2-x^2 \le f(x) \le x^2 for all xx, what is lim⁡x→0f(x)\displaystyle\lim_{x\to 0} f(x)?

  • A

    11

  • B

    −1-1

  • C

    Cannot be determined

  • D

    00

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Explanation

Both bounds approach 00 as x→0x \to 0, so by the Squeeze Theorem, lim⁡x→0f(x)=0\lim_{x\to 0} f(x) = 0.

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