Word Count : 294

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To find the values of \( a \) and \( b \) such that the following limit exists: \[ \lim_{x\to 0} \frac{a \tan(x) + bx}{x^3} \] We will need to use the Taylor series expansions for \( \tan(x) \) around \( x = 0 \). ### Step 1: Expand \( \tan(x) \) around \( x = 0 \) _________ ___ __________ ___ __________ _____ _________.
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