Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

lim (x².csc 2x.cot 2x) = ^x→ 0	A. 1
B.
C.
D. 4
E. 0

lim (x².csc 2x.cot 2x) = ^x→ 0	A. 1
B.
C.
D. 4
E. 0

$\\\displaystyle\lim_{x\to 0}\:(x^2.\csc 2x.\cot 2x)=\lim_{x\to 0}\:\left(x^2.\frac{\cot 2x}{\sin 2x}\right)=\lim_{x\to 0}\:\left(x^2.\frac{\cos 2x}{\sin^22x}\right)\\=\lim_{x\to 0}\:\left(\frac{x^2}{\sin^22x}.\cos 2x\right)=\lim_{x\to 0}\:\left(\frac{x}{\sin 2x}.\frac{x}{\sin 2x}.\cos 2x\right)=\frac12.\frac12.1=\frac14$