I have to find border of rational function: \lim_{x\rightarrow\infty}\frac{x^3+3x^2+2x}{x^2-x-6} What should I

Guy Rollins

Guy Rollins

Answered question

2022-02-16

I have to find border of rational function:
limxx3+3x2+2xx2x6
What should I do?

Answer & Explanation

greikkar5bu

greikkar5bu

Beginner2022-02-17Added 5 answers

First
limxx3(1+3x+2x2)x2(11x6x2)
Then divide top and bottom of the fraction by x2:
limxx(1+3x+2x2)(11x6x2)
This is valid as we know x0
Separate this fraction into two parts:
limx×limx(1+3x+2x2)(11x6x2)
The first part is obvious:
limx(x)=
For the second part, we consider each element as x:
limx3x=0
limx2x2=0
limx1x=0
limx6x2=0
So now we have
limx(1+3x+2x2)(11x6x2)=1+0+0100=1
Finally, we combine the two to say that
limxx3+3x2+2xx2x6=×1=
emeriinb4r

emeriinb4r

Beginner2022-02-18Added 10 answers

x3+3x2+2xx2x6x3x2=x
as x tends to infinity. Notice only the leading members (highest degrees) of the functions in denominator and numerator matter (That's if you have a rational function)

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