Find the Horizontal Asymptote of x^2+x-2 divided by x^2-3x-4.

Question

amistre64 · Answer

umm, we (err i) did that in the last post

anonymous · Answer

The last one was finding the range. this is the horizontal asymptote.

amistre64 · Answer

i found the HA during the process to test if it was within the range

anonymous · Answer

Mkaaay, I will look to that one for reference then. I'm sorry!

anonymous · Answer

There was so much going on on the last one. hehe :P

amistre64 · Answer

the idea is that when x is massively huge; the function is controlled top and bottom by the highest exponentail term

amistre64 · Answer

so; at large values of x
$$ \frac{x^2+x-2}{x^2-3x-4}=\frac{x^2}{x^2}$$
dont know a latex for "approximately

anonymous · Answer

Okay.

amistre64 · Answer

this simplifies to 1

anonymous · Answer

Oh, simple.

anonymous · Answer

So since numerator degree=denominator degree. It's the ratio of coefficients?

amistre64 · Answer

there are 3 conditions that can occur in rational expressions; the one we did was equal degrees

if the degrees are unequal, say; high top, low bottom$$\frac{x^6}{x^2}=x^4$$the top wins out and this thing goes up to infinity

if low top, high bottom$$\frac{x^3}{x^{10}}=\frac1{x^7}$$the bottom wins out and this thing goes to zero

amistre64 · Answer

yes, top equals bottom, it ration of first coeffs

anonymous · Answer

Ohhh, okay. :)