Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\displaystyle\lim_{x\to\,0}\frac{\tan x-x}{x^3}=$	A. 0
B. 1
C. \(\boldsymbol{\frac13}\)
D. 3
E. \(\boldsymbol{\frac16}\)

$\displaystyle\lim_{x\to\,0}\frac{\tan x-x}{x^3}\left(=\frac00\right)\overset{H}{=}\lim_{x\to\,0}\frac{\frac{1}{\cos^2x}-1}{3x^2}=\lim_{x\to\,0}\frac{\frac{1-\cos^2x}{\cos^2x}}{3x^2}=\lim_{x\to\,0}\frac{\tan^2x}{3x^2}=\frac13$

^{gricha - v8821 - 22.3.2023}