Word Count : 118

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We are asked to evaluate: [ \lim_{x \to 0} \frac{\tan x - \sin x}{x^3}. ] First, recall the Taylor expansions around (x = 0): [ \sin x = x _________ ________ _________ _______ __________ _________ _______ ___ _____ ______.
___ _________ __________ ___ ___ ____.
___ ____ _______ ________ _________ ___ _________ __________ ________ ____.
___ ___ ___ __________ ____ _____ ______.
_______ ______ __________ __________ _____ _____ ______ ____ ____ _______ ___ ________.
__________ _________ __________ ___ _________ _____ ___ _________.
______ ____ ___ ____ _____ _____ _______ ____ ___.
________ _____ ____ _____ _________ __________ ___ _________ _____ ________.
______ _______ _______ ____ __________ _____ _________ _____.
_______ ____ _________ ________ ______ ________ _________ _____.
_____.
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