If f(x) is the primitive ofsin⁡x3log⁡(1+3x)tan−1⁡x2ex3−1(x≠0) then limx→0 f′(x) is

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3/5

none of these

answer is D.

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Detailed Solution

limx→0 f′(x)=limx→0 sin⁡x3log⁡(1+3x)tan−1⁡x2ex3−1\=limx→0 3sin⁡x3x3×log⁡(1+3x)3x×xtan−1⁡x2x3ex3−1=3(1)(1)(1)2(1)=3

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