Nilai lim_(x→0)⁡ (sin ⁡4x+sin ⁡2x)/(3x cos⁡ x)=⋯

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Bahas Soal Matematika   »   Limit   ›  

Nilai \( \displaystyle \lim_{x \to 0} \ \frac{\sin 4x + \sin 2x}{3x \cos x} = \cdots \)

  1. 1/4
  2. 1/2
  3. 1
  4. 3/2
  5. 2

(EBTANAS SMA IPA 1996)

Pembahasan:

\begin{aligned} \lim_{x \to 0} \ \frac{\sin 4x + \sin 2x}{3x \cos x} &= \lim_{x \to 0} \ \frac{2 \sin \left( \frac{4x+2x}{2} \right) \cos \left( \frac{4x-2x}{2} \right) }{3x \cos x} \\[8pt] &= \lim_{x \to 0} \ \frac{2 \sin 3x \cos x }{3x \cos x} \\[8pt] &= \lim_{x \to 0} \ \frac{2 \sin 3x}{3x} \\[8pt] &= \frac{2 \cdot 3}{3} = 2 \end{aligned}

Jawaban E.