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Samenvatting analyse 1b1
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Een samenvatting over het vak analyse 1b1 uit de docentenopleiding wiskunde tweedegraads
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LimietenANALYSE 1B1
,Raaklijnen
De raaklijn van een grafiek is een lineaire lijn met als richtingscoëfficiënt de helling van dat pu
De formule van de helling van een (raak)lijn door twee punten P en Q is:
𝑦𝑞 − 𝑦𝑝
𝑚𝑝𝑞 =
𝑥𝑞 − 𝑥𝑝
𝑦𝑞 − 𝑦𝑝
lim
𝑥→∞ 𝑥𝑞 − 𝑥𝑝
,Raaklijnen
Hoe vinden wij dan de richtingscoëfficiënt in één punt?
Dus wij willen Q steeds dichter naar P verschuiven om zo dus die richtingscoëfficiënt te vinde
mogen nooit op elkaar liggen
Waarom mag dat niet?
𝑦𝑞 − 𝑦𝑝
lim
𝑥→∞ 𝑥𝑞 − 𝑥𝑝
Dit mag geen 0 zijn
, Richtingscoëfficiënt berekenen
Wat is de richtingscoëfficiënt in p(1,1) bij de formule 𝑦 = 𝑥 2
Wij gaan Q( dus steeds dichter naar P verschuiven
𝑥 2 −1
𝑚𝑝𝑞 = (de y van Q krijg je door 𝑥 2 )
𝑥−1
x m x m
2.0 3 0 1
1.5 2.5 0.5 1.5
1.1 2.1 0.9 1.9
1.01 2.01 0.99 1.99
1.001 2.001 0.999 1.999
𝑥 2 −1
𝑚𝑝𝑞 = =2
𝑥−1
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