$lim x \to 0 \frac{x^{2}}{sin x^{2}}$

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Solution

$lim x \to 0 \frac{x^{2}}{sin x^{2}}$
$= lim x \to 0 {(\frac{x}{sin x})}^{2}$
$= {(lim x \to 0 \frac{x}{sin x})}^{2}$
$= 1^{2}$
$= 1$

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