A student uses the linear approximation to estimate near

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A student uses the linear approximation L(x)=xL(x)=x to estimate arctan⁡x\arctan x near x=0x=0. Find the greatest value r>0r>0 such that the approximation error is guaranteed to be less than 0.0050.005 for all xx satisfying ∣x∣≤r|x|\le r. (a) ∣x∣≤0.15|x|\le 0.15 (b) ∣x∣≤0.25|x|\le 0.25 (c) ∣x∣≤0.17|x|\le 0.17 (d) ∣x∣≤0.10|x|\le 0.10

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