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AP Calculus AB· difficulty 3/5

Evaluate lim⁡h→04+h−2h\displaystyle\lim_{h\to 0}\dfrac{\sqrt{4+h}-2}{h}.

  • A

    22

  • B

    14\tfrac{1}{4}

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  • C

    11

  • D

    12\tfrac{1}{2}

Explanation

Multiply by conjugate: (4+h)−4h(4+h+2)=14+h+2→1/4\dfrac{(4+h) - 4}{h(\sqrt{4+h}+2)} = \dfrac{1}{\sqrt{4+h}+2} \to 1/4.

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