Question

help please!

Answer 1

We're here to help.

Answer 2

find the horzontal asymptotes

Answer 3

All you have to do is determine the behavior of \(f\) as it approaches both \(-\infty\) and \(\infty\), i.e.,\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=?\]

Answer 4

equal to 1 ?

Answer 5

y=1?

Answer 6

How did you get that?

Answer 7

x^2 / X^2 +3/x^2

Answer 8

everything divided by x^2

Answer 9

because highest power in the function is x^2

Answer 10

Recall that\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=\lim_{x\to\infty}\frac{x^2}{\sqrt{x^2}}=\lim_{x\to\infty}\frac{x^2}{|x|}=\lim_{x\to\infty}x=\infty.\]

Answer 11

So it has no horizontal asymptote as \(x\to\infty\). What about \(x\to-\infty\)?

Answer 12

same thing ?

Answer 13

Right.

Answer 14

thanks `