Question

Find the horizontal asymptote of f(x) = (2 x+5 x^3+3)/(4 x^3-4 x^2-2)

Answer 1

@Hero @ganeshie8 @mathstudent55 @sammixboo

Answer 2

I don't know how to approach the problem... but I know what a horizontal asymptote is

Answer 3

So my initial thought was to look at the degree of the denominator and the numerator but that doesn't seem to work for this one

Answer 4

To find the horizontal asymptote of a rational function, take the limit as x goes to infinity of the leading terms:

\[\lim_{x \rightarrow \infty}\frac{5x^3}{4x^3}\]

Answer 5

We are not doing limits... that is beyond my skill level

Answer 6

I am only in precalculus...

Answer 7

Is there another way to find the horizontal asymptote?

Answer 8

The textbook says to look at the degree of the numerator and denominator and compare the two... but I'm thinking that either the top or bottom need to be factored

Answer 9

Watch this video:
https://www.youtube.com/watch?v=c-yK2hUnSB0

Answer 10

OK, I watched that video. His example is an easy one though. I have one that is not as simple as just reducing the leading coefficients of the denominator and numerator

Answer 11

That is why I posted the problem about 15 hours ago.

Answer 12

It is that simple if you put the polynomials in standard form

Answer 13

Rewrite it as 5x^3+2x+3/4x^3-4x^2-2

Answer 14

Exactly

Answer 15

\[f(x) = \frac{5x^3 + 2x + 3}{4x^3 - 4x^2 - 2}\]

Answer 16

The denominator and numerator are both equal so I will take the leading coefficients

Answer 17

Horizontal asymptote at 5/4

Answer 18

That was a lot easier than I made it out to be. Thanks, I feel like I should have solved that within 15 hours

Answer 19

I should have trusted my natural instinct which was to reorder it but that is the same time I posted for help

Answer 20

The internet is your friend. Use all resources: Google, OS, Khan Academy, Patrick JMT, MIT OCW, Paul's Online Notes, etc.

Answer 21

Do you have a set of resources that you frequently use? I occasionally use Patrick JMT, Paul's Online Notes, and OS

Answer 22

I use the whole internet as a resource.