[tex] \lim_{x \to \ 0} \frac{2tan2x+sec 2x-1}{3tan2x-sec2x+1}[/tex]

Adapun dapat menggunakan teorema L'Hopital:
[tex]$\begin{align}\lim_{x\to0}\frac{2\tan2x+\sec2x-1}{3\tan2x-\sec2x+1}&=\lim_{x\to0}\frac{2\sin2x+1-\cos2x}{3\sin2x-1+\cos2x} \\ &\text{Mengunakan L'H\^opital} \\&=\lim_{x\to0}\frac{4\cos2x+0+2\sin2x}{6\cos2x-0-2\sin2x} \\ &=\frac{4\cos0+2\sin0}{6\cos0-2\sin0} \\ &=\frac{4.1+2.0}{6.1-2.0} \\ &=\frac46=\frac23\end{align}[/tex]