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Defining the Derivative and Using Derivative Notation

AP Calculus AB· difficulty 4/5

lim⁡h→0sin⁡(π3+h)−sin⁡(π3)h=\displaystyle \lim_{h \to 0} \frac{\sin\left(\frac{\pi}{3}+h\right) - \sin\left(\frac{\pi}{3}\right)}{h} =

  • A

    00

  • B

    12\frac{1}{2}

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  • C

    11

  • D

    32\frac{\sqrt{3}}{2}

Explanation

This is f′(π/3)f'(\pi/3) where f(x)=sin⁡xf(x)=\sin x, so cos⁡(π/3)=1/2\cos(\pi/3) = 1/2.

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