Consider the rational functions: r(x)=(2x−1)/((x^2)−x−2) , s(x)=((x^3)+27)/((x^2)+4) , t(x)=((x^3)−9x)/(x+2)

Alyce Wilkinson 2021-09-11 Answered

Consider the following rational functions: r(x)=2x1(x2)x2
s(x)=(x3)+27(x2)+4
t(x)=(x3)9xx+2
u(x)=(x2)+x6(x2)25
w(x)=(x3)+(6x2)+9xx+3
Which of these rational functions has a horizontal asymptote?

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Expert Answer

Ezra Herbert
Answered 2021-09-12 Author has 99 answers
r(x)=2x1(x2)x2=2x1(x2)(x+1)
s(x)=(x3)+27(x2)+4=(x+3)(x+9+3x)(x2)+4
t(x)=(x3)9xx+2=x(x3)(x+3)x+2
u(x)=(x2)+x6(x2)25=(x2)(x+3)(x5)(x+5)
w(x)=(x3)+(6x2)+9xx+3=x(x+3)
r,t and u have horizontal asymptotes
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