Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De limiet $https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0} \: \frac {3.Bgtan \:x\,-\:x}{2x\,-\,Bgsin \:x}$ is gelijk aan	A. 1
	B. 2
	C. 3
	D. − 3
	E. 1,5

[ 5-7107 - op net sinds 12.3.2020-(E)-12.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0} \: \frac {3.\arctan \,x\,-\:x}{2x\,-\,\arcsin \,x}$ is equal to	A. 1
	B. 2
	C. 3
	D. −3
	E. 1.5

Oplossing - Solution

$\displaystyle\lim_{x\to 0}\:\frac{3.Bgtan\:x\,-\:x}{2x\,-\,Bgsin\:x}\left(=\frac00\right)\overset{H}{=}\displaystyle\lim_{x\to 0}\:\frac{\frac{3}{1+x^2}-1}{2-\frac{1}{\sqrt{1-x^2}}}=\frac{3-1}{2-1}=2$