Асимптоты у=(x^3-1)/4x^2 y=9x/9-x^2 y=(x^2-x+1)/x-1. Created by VasyanDoctor. matematika-ru

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VasyanDoctor @VasyanDoctor

July 2022 1 8 Report

Асимптоты
у=(x^3-1)/4x^2
y=9x/9-x^2
y=(x^2-x+1)/x-1

Answers & Comments

sedinalana

Verified answer

1
у=(x^3-1)/4x^2
D(f)∈(-∞;0) U (0;∞)
x=0-вертикальная асиптота
k=lim(x³-1)/4x³=lim(1/4-1/4x³)=1/4-0=1/4
   x→∞
b=lim[(x³-1)/4x²-x/4]=lim(x³-1-x³)/4x²=lim(-1/4x^2)=0
   x→∞
y=x/4-наклонная асиптота
2
y=9x/9-x^2
D(f)∈(-∞;-3) U (-3;3) U (3;∞)
x=-3 и х=3-вертикальные асиптоты
k=lim9x/[x(9-x²)]=lim9/(9-x²)=0
   x→∞
b=lim(9/(9-x²)-0)=0
   x→∞
наклонных асиптот нет
3
y=(x^2-x+1)/x-1
D(f)∈(-∞;1) U (1;∞)
x=1 вертикальная асиптота
k=lim(x²-x+1)/[x(x-1)]=lim(1+1/(x²-x))=1
   x→∞
b=lim[(x²-x+1)/(x-1)-x]=lim1/(x-1)=0
   x→∞
y=x наклонная асиптота

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