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[tex]\displaystyle \lim_{x\to0}\frac{x^2+\sin^22x}{x^2\cos2x}=\lim_{x\to0}\frac{x^2+\sin^22x}{x^2}\cdot\frac{1}{\cos2x}\\\lim_{x\to0}\frac{x^2+\sin^22x}{x^2\cos2x}=\lim_{x\to0}\left(1+\left(\frac{\sin2x}{x}\right)^2\right)\cdot\lim_{x\to0}\frac{1}{\cos2x}\\\lim_{x\to0}\frac{x^2+\sin^22x}{x^2\cos2x}=(1+(2)^2)\cdot\frac{1}{\cos2(0)}\\\lim_{x\to0}\frac{x^2+\sin^22x}{x^2\cos2x}=(1+4)\cdot\frac{1}{\cos0}\\\boxed{\boxed{\lim_{x\to0}\frac{x^2+\sin^22x}{x^2\cos2x}=5}}[/tex]

Limit Fungsi Trigonometri.
Kelompok peminatan kelas XII kurikulum 2013 revisi 2016.

lim x→0 (x² + sin² 2x) / (x² cos 2x)
= lim x→0 [1 + (sin² 2x) / x²] / cos 2x
= lim x→0 [1 + (sin 2x / x)²] / cos 2x
= [1 + (sin 0 / 0)²] / cos 0
= (1 + 0 / 0) / 1

0 / 0 merupakan bentuk tak tentu. Gunakan aturan L'Hôpital!
= lim x→0 [1 + (2 cos 2x / 1)²] / cos 2x
= [1 + (2 cos 0 / 1)²] / cos 0
= (1 + 4) / 1 = 5