Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\\\text{Gegeven : }\;f(x)=\frac{9-x^2}{3x-x^2}\\\\\text{Dan is : }\;\displaystyle \lim_{x \to 3}f(x)+\displaystyle \lim_{x\to +\infty}f(x) =$	A. 1
	B. 2
	C. 3
	D. 4
	E.

[ 5-6946 - op net sinds 23.3.12-(E)-17.11.2024 ]

Translation in E N G L I S H

$\\\text{Given : }\;f(x)=\frac{9-x^2}{3x-x^2}\\\\\text{then : }\;\displaystyle \lim_{x \to 3}f(x)+\displaystyle \lim_{x\to \infty}f(x) =$	A. 1
	B. 2
	C. 3
	D. 4
	E. ∞

Oplossing - Solution

$\begin{aligned}\lim_{x \to \, 3}\: \frac{9-x^2}{3x-x^2 }=\lim_{x \to \, 3}\: \frac{(3-x)(3+x)}{x(3-x)}=\lim_{x \to \, 3}\: \frac{3+x}{x}=\frac 63 = 2\\\lim_{x \to \, +\infty }\: \frac{9-x^2}{3x-x^2 }=\lim_{x \to \, +\infty }\: \frac{-x^2}{-x^2 }= +1\end{aligned}$