Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle\lim_{x \to -1}\frac {x^3+1} {x^4-1}$ is gelijk aan	A. 1
	B. − 1
	C. − 0,75
	D. 0
	E.

[ 5-5134 - op net sinds 11.3.2020-(E)-4.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle\lim_{x \to -1}\frac {x^3+1} {x^4-1} =$	A. 1
	B. − 1
	C. − 0.75
	D. 0
	E. − ∞

Oplossing - Solution

$\\\displaystyle\lim_{x\to-1}\,\frac{x^3+1}{x^4-1}=\displaystyle\lim_{x\to-1}\,\frac{(x+1)(x^2-x+1)}{(x^2+1)(x+1)(x-1)}=\displaystyle\lim_{x\to-1}\,\frac{x^2-x+1}{(x^2+1)(x-1)}\\=\frac{1+\!1+1}{2.(-2)}=-\frac34$