Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to \frac{\pi}{2}} \: \frac {x - \frac {\pi}{2}} {\cos x}$ is gelijk aan	A. 1
B. − 1
C. 0
D.
E.

$\displaystyle \lim_{x \to \frac{\pi}{2}} \: \frac {x - \frac {\pi}{2}} {\cos x}$ is equal to	A. 1
	B. − 1
	C. 0
	D.
	E. ∞

1^ste manier : zonder de regel van de L'Hospital
$\displaystyle\lim_{x\to\frac{\pi}{2}}\:\frac{x-\frac{\pi}{2}}{\cos x}=\displaystyle\lim_{x\to\frac{\pi}{2}}\:\frac{x-\frac{\pi}{2}}{\sin\left(\frac{\pi}{2}-x\right)}=-\displaystyle\lim_{x\to\frac{\pi}{2}}\:\frac{\frac{\pi}{2}-x}{\sin\left(\frac{\pi}{2}-x\right)}=-1$
2^de manier : met de regel van de L'Hospital
$\displaystyle\lim_{x\to\frac{\pi}{2}}\:\frac{x-\frac{\pi}{2}}{\cos x}\left( =\frac00\right)\overset{H}{=}\displaystyle\lim_{x\to\frac{\pi}{2}}\:\frac{1}{-\sin x}=\frac{1}{-1} =-1$