Wiskunde Multiple Choice Vraag

$\displaystyle\lim_{x\to\frac12}\left[(4x^2-1).\cot(2x-1)\right]=$	A. 16
B. 2
C. 8
D. 4
E. 0

$\displaystyle\lim_{x\to\frac12}\left[(4x^2-1).\cot(2x-1)\right]=$

$\begin{matrix}\displaystyle\lim_{x\to\frac12}\left[(4x^2-1).\cot(2x-1)\right]\\=\displaystyle\lim_{x\to\frac12}\frac{4x^2-1}{\tan(2x-1)}\left(=\frac00\right)\\\overset{H}{=}\displaystyle\lim_{x\to\frac12}\frac{8x}{\frac{2}{\cos^2(2x-1)}}=\frac{4}{2}=2\quad\end{matrix}$