Local Linearity and Linearization

AP Calculus AB· difficulty 2/5

Use L(x)=1+x2L(x) = 1 + \tfrac{x}{2} (linearization of 1+x\sqrt{1+x} at x=0x = 0) to estimate 1.04\sqrt{1.04}.

  • A

    1.081.08

  • B

    1.021.02

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  • C

    1.201.20

  • D

    1.041.04

Explanation

L(0.04)=1+0.02=1.02L(0.04) = 1 + 0.02 = 1.02.

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