What is ?
Answer and explanation
Correct answer: B.
- Step 1: Recall the standard trigonometric limits as : , , and .
- Step 2: Rewrite the rational expression to isolate these limits: $dfrac{sin(3x) an(2x)}{1 - cos x} = dfrac{frac{sin(3x)}{3x} imes frac{ an(2x)}{2x}}{frac{1 - cos x}{x^2}} imes dfrac{(3x)(2x)}{x^2}$.
- Step 3: Evaluate the limit by substitution: .
Answer
.
Why not the others: Other values apply standard small-angle approximations without accounting for the coefficients, or drop the denominator expansion of .
Practise more Basic results.
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