Squeeze Theorem

AP Calculus AB· difficulty 2/5

Evaluate limx0sin(5x)x\displaystyle\lim_{x \to 0}\dfrac{\sin(5x)}{x}.

  • A

    15\tfrac{1}{5}

  • B

    11

  • C

    00

  • D

    55

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Explanation

Rewrite: sin(5x)x=5sin(5x)5x\dfrac{\sin(5x)}{x} = 5 \cdot \dfrac{\sin(5x)}{5x}. As x0x \to 0, sin(5x)/(5x)1\sin(5x)/(5x) \to 1, so the limit is 55.

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