Evaluate the trigonometric limit: lim (x -> 0) [sin(7x) / (2x)].
Answer and explanation
Correct answer: A. 7/2
- Step 1: Apply the standard trigonometric limit theorem: lim (u -> 0) [sin(u) / u] = 1.
- Step 2: Rewrite the expression: lim (x -> 0) [(7/2) * (sin(7x) / (7x))].
- Step 3: Factor out the constant multiplier: (7/2) * 1 = 7/2.
Answer
7/2.
Why not the others: '2/7' inverts the numerator and denominator coefficients; '0' improperly sets x to 0 without resolving the indeterminate 0/0 quotient; '7' overlooks the denominator factor of 2.
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