Word Count : 195

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i) To check whether $\lim_{x \to 0} \frac{|x|}{x}$ exists, we examine the left-hand and right-hand limits separately. Right-hand limit: $x \to 0^+$ $$ \lim_{x \to 0^+} \frac{|x|}{x} = \lim_{x \to 0^+} \frac{x}{x} = \lim_{x \to 0^+} 1 = 1 $$ Left-hand limit: $x \to 0^-$ $$ \lim_{x \to ___ ____ _________ ____ _____ ___ _________ ____ _______ ______.
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