Word Count : 180

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We are asked to find (a) and (b) such that [ \lim_{x \to 0} \frac{a \tan x + b x}{x^3} \text{ exists.} ] Start by expanding (\tan x) as a Maclaurin series: [ \tan x = ___ ______ _________ ____ ___ ___ ____ ___ ________ __________ _____.
_____ ______ ______ _______ _______ ____ ___ ______.
________ ____ _____ ________ _________ ___.
________ _______ ________ _____ ____ ____ ___ __________ ______ _______ ________ _________.
___ ____ _________ _____ _________.
_________ _______ ________ ________ ________ ________ ______ __________ ______ ______ _____ _________.
____ __________ __________ _________ ______.
_______ _______ ____ ______ ______ ___ __________ ___ ___ ____ ______.
________ _______ ______ ____ ______ ___.
________ __________ __________ _______ _________ ________ ____ ____.
_______ _________ ____ ________ ________ ___ __________ _____ ____.
_____ ________ ____ ______ __________ _________ __________ ___ ________.
______ ___ ________ ___ ______.
_______ _________ ______ _______ ________ ______ ________ ______ ________ ________ ___ ___.
____ _________ ____ ____ ___ ____ __________ _________ _____.
__________ _________ ___ ___ ___ _____ ________ ________ _________.
______ ____ _____ __________ __________.
___ ____.
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