Berikut ini adalah kumpulan soal mengenai Limit Trigonometri tingkat dasar. Jika ada jawaban yang salah, mohon dikoreksi melalui komentar. Terima kasih.
No. 1
{\displaystyle\lim_{x\to0}\dfrac{\cos3x-\cos x}{\tan^22x}=} ....
\(\begin{aligned}
\displaystyle\lim_{x\to0}\dfrac{\cos3x-\cos x}{\tan^22x}&=\displaystyle\lim_{x\to0}\dfrac{-2\sin\left(\dfrac{3x+x}2\right)\sin\left(\dfrac{3x-x}2\right)}{\tan^22x}\\[8pt]
&=\displaystyle\lim_{x\to0}\dfrac{-2\sin2x\sin x}{\tan^22x}\\[8pt]
&=-2\displaystyle\lim_{x\to0}\dfrac{\sin2x}{\tan2x}\cdot\dfrac{\sin x}{\tan2x}\\[8pt]
&=-2\cdot\dfrac22\cdot\dfrac12\\
&=\boxed{\boxed{-1}}
\end{aligned}\)
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