Question

Find the horizontal asymptote of (x^2)/((x^4)+2)

Answer 1

\[\frac{ x^2 }{ \sqrt{x^4+2} }\]

Answer 2

hint: x^2 = sqrt(x^4)

Answer 3

If the degree of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y=0)

Answer 4

how do i figure out if \[\sqrt{x^4+2}\] is a bigger or smaller degree?

Answer 5

What is the degree in the denominator?

Answer 6

4?

Answer 7

Or is it 2, since it's sqrt?

Answer 8

correct, it's 4

Answer 9

do you understand what horizontal asymptote is?

Answer 10

Yep, the limit as x tends to - or + infinity (where y get close to in the distance)

Answer 11

Yes

Answer 12

so here are some steps to help you find the horizontal asymptote:
1) Put equation or function in y= form.

2) Multiply out (expand) any factored polynomials in the numerator or denominator.

3) Remove everything except the terms with the biggest exponents of x found in the numerator and denominator. These are the "dominant" terms.

Answer 13

I'm just having trouble expanding the denominator
\[\sqrt{x^4+2}\]

Answer 14

Refer to the attachment.