Computing Limits — Question 4

Question 4

Evaluate the limit: $$\lim_{x \to 0} \frac{\sin(3x)}{x}$$

Question 4 - Solution

We are asked to evaluate: $$\lim_{x \to 0} \frac{\sin(3x)}{x}$$

Step 1: Use standard limit identity

Recall the standard identity: $$\lim_{x \to 0} \frac{\sin(kx)}{x} = k$$

This applies directly here with $k = 3$.

$$\lim_{x \to 0} \frac{\sin(3x)}{x} = 3$$

Answer: $\boxed{3}$