Using L'Hôpital's rule, what is the limit lim_{x -> 0} (sin(4x) / (2x))?
Answer and explanation
Correct answer: C. 2
Direct substitution gives 0/0 (indeterminate). Differentiating numerator and denominator with respect to x: d/dx[sin(4x)] = 4cos(4x), and d/dx[2x] = 2. Applying L'Hôpital's rule: lim_{x -> 0} [4cos(4x) / 2] = 4*cos(0) / 2 = 4(1) / 2 = 2.
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