To approximate by the tangent line to at

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

To approximate sin⁡0.2\sin 0.2 by the tangent line to sin⁡x\sin x at x=0x=0, let MM be the maximum of ∣sin⁡′′(x)∣\lvert\sin''(x)\rvert on the interval [0,0.2][0,0.2]. Which of the following is an upper bound for the magnitude of the error in this approximation? (a) 0.020.02 (b) 0.0040.004 (c) 0.0080.008 (d) 0.00040.0004

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