Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle\: \lim_{x \to 0}\frac{4^x-(\frac 12)^x}{x}$ is gelijk aan	A. ln 2
	B. 2.ln 2
	C. 3.ln 2
	D. 4.ln 2
	E. 0

[ 6-6822 - op net sinds 11.12.11-(E)-3.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\large \dpi{110}\displaystyle\: \lim_{x \to 0}\frac{4^x-(\frac 12)^x}{x}$ equals	A. ln 2
	B. 2 (ln 2)
	C. 3 (ln 2)
	D. 4 (ln 2)
	E. 0

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\\displaystyle\: \lim_{x \to 0}\frac{4^x-(\frac 12)^x}{x}\left ( =\frac{1-1}{0} \right )\overset{H}{=}\displaystyle\: \lim_{x \to 0}\frac{4^x.\ln 4-(\frac 12)^x.\ln (\frac12)}{1}\\=4^0.\ln 4-(\frac 12)^0.\ln(\frac 12)=\ln 4 + \ln 2 = 2.\ln 2 + \ln 2 = 3.\ln 2$