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Substitution Method to Remove Indeterminate Form

Calculate the...

Question

Calculate the following limits.
$lim x \to 0 \frac{s i n 3 x}{2 x} .$

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Solution

$lim x \to 0 \frac{sin 3 x}{2 x}$

$= lim x \to 0 \frac{sin 3 x}{3 x} \frac{3 x}{2 x}$

$= \frac{3}{2}$

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