Discussion

The value of \( \lim_{x \to 0} \dfrac{\sin 5x}{3x} \) is

Answer: A

Write the quotient so that the standard limit appears with a matching argument:

\[ \frac{\sin 5x}{3x} \;=\; \frac{5}{3}\cdot\frac{\sin 5x}{5x}. \]

Since \( \sin\theta/\theta \to 1 \) as \( \theta \to 0 \), the second factor tends to one and

\[ \lim_{x \to 0} \frac{\sin 5x}{3x} \;=\; \frac{5}{3}. \]

The reciprocal \( 3/5 \) comes of matching the arguments the wrong way round

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