Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0}\: \frac{4x.\sin^23x}{\cos5x.\tan^32x}$ is gelijk aan	A.
B. 0,8
C. 36
D. 4,5
E. 8

$\displaystyle \lim_{x \to 0}\: \frac{4x.\sin^23x}{\cos5x.\tan^32x}$ is equal to	A. ∞
	B. 0.8
	C. 36
	D. 4.5
	E. 8

$\displaystyle\lim_{x\to 0}\frac{4x.\sin^23x}{\cos5x.\tan^32x}=\lim_{x\to 0}\frac{4}{\cos 5x}.\lim_{x\to 0}\frac{x.\sin^23x}{\tan^32x}=4.\lim_{x\to 0}\frac{x.\sin 3x.\sin 3x}{\tan 2x.\tan 2x.\tan 2x}$

$=4\displaystyle\lim_{x\to 0}\left(\frac{\sin 3x}{3x}.\frac{\sin 3x}{3x}.\frac{2x}{\tan 2x}.\frac{2x}{\tan 2x}.\frac{2x}{\tan 2x}.\frac{x.3x.3x}{2x.2x.2x}\right)=4.1.1.1.1.1.\frac98=\frac 92$