,Hoofdstuk 13 Limieten en Asymptoten (V6 Wis B) Pagina 2 van 17
LES 2 : ASYMPTOTEN
DEFINITIE ASYMPTOTEN
Er zijn twee soorten asymptoten :
(1) Horizontale Asymptoot (HA)
• lim 𝑓𝑓(𝑥𝑥) 𝑜𝑜𝑜𝑜 lim 𝑓𝑓(𝑥𝑥) (d.w.z. voor x een groot getal invullen)
𝑥𝑥→∞ 𝑥𝑥→−∞
• Vergelijking : y = getal
, Hoofdstuk 13 Limieten en Asymptoten (V6 Wis B) Pagina 3 van 17
Nu kun je pas de asymptoten bepalen
(1) Horizontale Asymptoot (HA)
24
60𝑥𝑥−24 60− 60−0
1. lim = lim 6
𝑥𝑥
= = 20 Dus HA : y = 20
𝑥𝑥→∞ 3𝑥𝑥+6 𝑥𝑥→∞ 3+𝑥𝑥 3+0
24
60𝑥𝑥−24 60− 60−0
2. lim = lim 𝑥𝑥
6 = = −20 Dus HA : y = -20
𝑥𝑥→−∞ −3𝑥𝑥−6 𝑥𝑥→∞ −3−𝑥𝑥 −3−0
(2) Verticale Asymptoot (VA)
3𝑥𝑥 + 6 = 0 → 𝑥𝑥 = −2. Dus VA : x = -2
Nu kun je de grafiek tekenen :
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