Nilai lim_(x→0)⁡ (3x tan ⁡2x)/(1-cos⁡ 4x)=⋯

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Bahas Soal Matematika   »   Limit   ›  

Nilai \( \displaystyle \lim_{x \to 0} \ \frac{3x \tan 2x}{1 - \cos 4x} = \cdots \)

Pembahasan:

\begin{aligned} \lim_{x \to 0} \ \frac{3x \tan 2x}{1 - \cos 4x} &= \lim_{x \to 0} \ \frac{3x \tan 2x}{2\sin^2 2x} \\[8pt] &= \lim_{x \to 0} \ \frac{3x}{2 \sin 2x} \cdot \lim_{x \to 0} \ \frac{\tan 2x}{\sin 2x} \\[8pt] &= \frac{3}{2 \cdot 2} \cdot \frac{2}{2} = \frac{3}{4} \end{aligned}