Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle \lim_{x \to 0}\, \frac{x^2}{1-\sec 2x}=$	A. 1
	B. 2
	C. − 1
	D.
	E.

[ 5-6211 - op net sinds 11.8.2020-(E)-4.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle \lim_{x \to 0}\, \frac{x^2}{1-\sec 2x}=$	A. 1
	B. 2
	C. − 1
	D.
	E.

Oplossing - Solution

$\\\displaystyle\lim_{x\to 0}\,\frac{x^2}{1-\sec 2x}=\displaystyle\lim_{x\to 0}\,\frac{x^2.\cos2x}{\cos^2x-1}=\displaystyle\lim_{x\to 0}\,\frac{x^2.\cos2x}{-2\sin^2x}\\=\displaystyle\lim_{x\to 0}\,\frac{x^2}{\sin^2x}.\displaystyle\lim_{x\to 0}\,\frac{\cos 2x}{-2}=1.\frac{1}{-2}=-\frac12$