Evaluate the trigonometric limit: lim (x -> 0) [sin(5x) / (3x)].
Answer and explanation
Correct answer: D. 5/3
- Step 1: Recall the standard trigonometric limit theorem: lim (u -> 0) [sin(u) / u] = 1.
- Step 2: Rewrite the given expression: lim (x -> 0) [(5/3) * (sin(5x) / (5x))].
- Step 3: Factor out the constant: (5/3) lim (x -> 0) [sin(5x) / (5x)] = (5/3) 1 = 5/3.
Answer
5/3.
Why not the others: '3/5' inverts the numerator and denominator coefficients; '0' assumes direct evaluation without recognizing the indeterminate 0/0 form; '1' fails to scale by the ratio of the coefficients 5/3.
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