Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{{x \to 0}}\;\frac {\log_2\, (1-x^2)} {\log_4\, (\cos x)} =$	A. 1
B. 2
C. 4
D. − 2
E. − 4
F.

$\\\displaystyle\lim_{{x\to 0}}\;\frac{\log_2\,(1-x^2)}{\log_4\,(\cos x)}\left(=\frac00\right)\overset{H}{=}\displaystyle\lim_{{x\to 0}}\;\frac{\frac{1.(-2x)}{(1-x^2).\ln2}}{\frac{1.(-\sin x)}{\cos x.\ln4}}=\displaystyle\lim_{{x\to 0}}\;\frac{2x.\cos x.\ln2^2}{(1-x^2).\ln2.\sin x}\\=\displaystyle\lim_{{x\to 0}}\;\frac{2(\cos x).2.\ln2}{(1-x^2).\ln2}.\displaystyle\lim_{{x\to 0}}\;\frac{x}{\sin x}=\frac{2.1.2}{1}.1=4$