Word Count : 247

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नीचे प्रत्येक कथन के लिए सत्य/असत्य तथा संक्षिप्त कारण दिए जा रहे हैं। --- ### (i) [ \lim_{x\to 0}\frac{x^2\sin\left(\frac{1}{x}\right)}{\sin x}=1 ] असत्य। कारण: [ \frac{x^2\sin(1/x)}{\sin x} = x\cdot \sin(1/x)\cdot \frac{x}{\sin x} ] जब (x\to 0), तब (\frac{x}{\sin x}\to 1), लेकिन (x\sin(1/x)\to 0) क्योंकि (|\sin(1/x)|\le 1)। अतः पूरा मान (0) ____ _______ ___ ________ ____.
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