Evaluate: lim_{x -> 0} (sin(4x)) / (2x).
Answer and explanation
Correct answer: C. 2
- Step 1: Rewrite expression: (sin(4x) / (4x)) (4x / 2x). Step 2. Apply fundamental trigonometric limit: lim_{u -> 0} sin(u)/u = 1. Step 3. Evaluate remaining factor: 4x / 2x = 2. Step 4. Multiply: 1 2 = 2. Answer: 2. Why not the others: 1 assumes standard limit without scaling; 4 ignores division by 2; 1/2 inverts the ratio.
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