Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\lim_{x \to 1}\; \frac {Bgcos\:x} {\sqrt{2\,-\,2x}}$ is gelijk aan	A. 1
	B. 2
	C. − 2
	D. 4
	E. 0

[ 5-5030 - op net sinds 3.6.2020-(E)-12.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\lim_{x \to 1}\; \frac {\arctan x} {\sqrt{2\,-\,2x}}$	A. 1
	B. 2
	C. − 2
	D. 4
	E. 0

Oplossing - Solution

$\\\lim_{x\to 1}\;\frac{Bgcos\:x}{\sqrt{2\,-\,2x}}\left(=\frac00\right)\overset{H}{=}\lim_{x\to 1}\;\frac{-\frac{1}{\sqrt{1-x^2}}}{\frac{-2}{\sqrt{2-2x}}}=\lim_{x\to 1}\;\frac{\sqrt{2-2x}}{\sqrt{1-x^2}}\\=\lim_{x\to 1}\;\frac{\sqrt2\sqrt{1-x}}{\sqrt{1-x}\sqrt{1+x}}=\lim_{x\to 1}\;\frac{}{}\frac{\sqrt2}{\sqrt{1+x}}=\frac{\sqrt2}{\sqrt{1+1}}=1$