Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Welke limiet levert een reëel getal op, verschillend van 0 ?	A. $https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0}\: \frac{\tan x}{x^n}$
	B. $https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0}\: \frac{\tan x}{x^n}$
	C. $https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0}\: \frac{\tan x}{x^n}$
	D. $https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{x \to 0}\: \frac{\tan x}{x^n}$
	E. geen enkele van deze vier limieten

[ 6-8821 - op net sinds 22.3.2023-(E)-4.11.2024 ]

Translation in E N G L I S H

IN CONSTRUCTION

Oplossing - Solution

$\displaystyle \lim_{x \to \, 0}\frac{\tan x -x}{x^3}\left ( =\frac 00 \right )\overset{H}{=}\displaystyle \lim_{x \to \,0}\frac{\frac{1}{\cos^2x}-1}{3x^2}= \displaystyle \lim_{x \to \,0}\frac{\frac{1-\cos^2x}{\cos^2 x}}{3x^2}= \displaystyle\lim_{x \to \, 0}\frac{\tan^2x}{3x^2} =\frac13$