alleryEvaluate $\displaystyle\lim_{x \to 0} \dfrac{\sin 3x}{x}$.
A$1$
B$3$
C$\infty$
D$0$
Answer & Solution
Correct answer: B. $3$
Using the standard limit $\lim_{u\to 0} \dfrac{\sin u}{u} = 1$, write $\dfrac{\sin 3x}{x} = 3 \cdot \dfrac{\sin 3x}{3x}$.
As $x \to 0$, the second factor $\to 1$, giving $3$.
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