Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 9} \: {\frac{\sqrt x - 3}{x-9}$ is gelijk aan	A.
	B.
	C. 3
	D. 6
	E. 9

[ 5-5985 - op net sinds 27.10.13-(E)-30.10.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 9} \: {\frac{\sqrt x - 3}{x-9}$ is equal to	A.
	B.
	C. 3
	D. 6
	E. 9

Oplossing - Solution

$\\\lim_{x\to 9}\frac{\sqrt{x}\!-\!3}{x-9}\!\!=\!\!\lim_{x\to 9}\frac{(\sqrt{x}-\!3)(\sqrt{x}+\!3)}{(x-9)(\sqrt{x}+3)}\!\!=\!\!\lim_{x\to 9}\frac{x-9}{(x\!-\!9)(\sqrt{x}\!+\!3)}\!=\!\lim_{x\to 9}\frac{1}{\sqrt{x}+3}\!=\!\frac{1}{3\!+\!3}\!=$