Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 1} \: \frac {\log x} {x\,-\,1}$ is gelijk aan	A. 1
	B. ln 10
	C. log e
	D. 0
	E. 0,5

[ 6-6628 - op net sinds 4.11.13-(E)-30.10.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 1} \: \frac {\log x} {x\,-\,1}$ is equal to	A. 1
	B. ln 10
	C. log e
	D. 0
	E. 0.5

Oplossing - Solution

${\color{Cyan} \mid } \newline {\color{DarkGreen} \lim_{x \to 1}\frac{log\: x}{x-1}\left ( =\frac{0}{0} \right )= \lim_{x \to 1}\frac{\frac{1}{x\cdot ln\: 10}}{1}= \frac{1}{ln\: 10}=log\: e }$