Evaluate the limit: lim_(x -> 0) [sin(5x) / (2x)].
Answer and explanation
Correct answer: B. 5/2
- Step 1: Apply the fundamental trigonometric limit: lim_(u -> 0) [sin(u) / u] = 1.
- Step 2: Rewrite the expression: [sin(5x) / (2x)] = (5/2) * [sin(5x) / (5x)].
- Step 3: Take the limit as x -> 0: (5/2) * 1 = 5/2.
Answer
5/2.
Why not the others: '0' substitutes x=0 into the numerator without applying the limit quotient; '1' overlooks the scalar coefficients 5 and 2; '2/5' inverts the numerator and denominator coefficients.
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