Find the horizontal and vertical asymptotes of the curve.

Y= x^2 + 3/3x^2 − 26x − 9

Question

Find the horizontal and vertical asymptotes of the curve.

Y= x^2 + 3/3x^2 − 26x − 9

anonymous · Answer

Hey loco!! Where have you been man?!

anonymous · Answer

Anwar!!! What's up? Busy man.

anonymous · Answer

Still have one more final exam to do, then I can go see my family for the first time in 17 weeks.

anonymous · Answer

Oh... wow. I'm taking Calc I as a summer class.

anonymous · Answer

Oh your summer session has already started?!

anonymous · Answer

Yeah, going into the 3rd week.

anonymous · Answer

Let's get to your question now. Is the function $y=\frac{x^2 + 3}{3x^2 − 26x − 9}$?

anonymous · Answer

Yep

anonymous · Answer

Good. So let's start by vertical asymptotes. The vertical asymptotes of a rational function occurs at the zeros of the denominator. So, we have to find when the denominator is $0$ by solving $3x2−26x−9=0 \implies (3x+1)(x-9)=0$ That's $x=-\frac{1}{3}$ or $x=9$. Since non of them is a zero of the numirator then these two values would be your vertical asymptotes.

anonymous · Answer

For horizontal asymptotes, you have to take the limit of the function as it goes to infinity, that's:
$$\lim_{x \rightarrow \infty}{x^2+3 \over 3x^2-26x-9}$$, the limit of this is just the coffieceint of the hieghst degree of x in the numerator over the coffieceint of the hieghst degree in the denominator, which is $\frac{1}{3}$.

anonymous · Answer

I don't understand the horizontal asymptote part.

anonymous · Answer

When you want to find the horizontal asymptotes of a function, you're actually studying its behavior as it goes to infinty. So we took the limit as x goes to infinity. Now, let's focus on how we can find the limit of a rational function, as ours, when it's approaching infinty. In our case the degree of the numerator is the same as the degree of denominator. So, the limit will be just the coefficients of x^2, which are 1 in the numerator and 3 in the denominator.

anonymous · Answer

Oh ok... good explanation.

anonymous · Answer

Really?! :D

anonymous · Answer

Yes!

anonymous · Answer

Find the limit. (If you need to use or –, enter INFINITY or –INFINITY, respectively.) http://www.webassign.net/cgi-bin/symimage.cgi?expr=lim_%28x-%3Einfinity%29%20text%28%20%20%29%20%28x%2B2%29%2Fsqrt%284%20x%5E2%2B1%29

anonymous · Answer

Can you help me with this one?

anonymous · Answer

I have to go now! I'll help you when I come back.

anonymous · Answer

I got it. I have another problem though. Thanks!