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Local Linearity and Linearization

AP Calculus AB· difficulty 2/5

The linearization of sin⁡x\sin x at x=0x = 0 is

  • A

    L(x)=1−x2/2L(x) = 1 - x^2/2

  • B

    L(x)=1L(x) = 1

  • C

    L(x)=0L(x) = 0

  • D

    L(x)=xL(x) = x

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Explanation

sin⁡0=0\sin 0 = 0, sin⁡′(0)=1\sin'(0) = 1. L(x)=0+1⋅x=xL(x) = 0 + 1 \cdot x = x.

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