Wednesday

July 30, 2014

July 30, 2014

Posted by **brian** on Wednesday, September 27, 2006 at 6:12pm.

y = (x-9) / sqr(4x^2 + 3x+ 2)

What happens to y as x goes to +/- infinity? Specifically, is y approaching some limit from above or below?

??

I see your question was to just find the horizontal asymptotes and not to evaluate the function's approach to them.

The denominator has no real zeroes, so it's always positive. For large x the denominator behaves like |x| and the numerator is just x. The limits that need to be checked are

lim x-> +/-infinity x/|x|

Does that help?

so

sqr(4x^2 + 3x +2) is equivalent to |x|

Check that, it for large x it behaves like 2|x| -I missed the 4.

thx

**Related Questions**

horizontal asymptote - Find the horizontal asymptotes of the function's graph y...

Calculus - what happens when the limit goes to infinity 4x-6sqrt(x)

Calculus - Check my work please? Determine if f(x)= (x^2-3x+2)/(1+x^2) has a ...

calculus - If f has domain [0, infinity) and has no horizontal asymptotes, then ...

Math-precalc - Is it possible to find a rational function that has x-intercepts...

Math - the lim [as x goes to infinity] (.25)^x =0?? Yes, the limit is zero. The ...

math - Hi, I have a math question that I need help with: g:-> 3(1.3)^x State ...

Calculus - What is the limit? 1. limit as x goes to POSITIVE infinity (10x+8)/(...

calculus - limit as x approaches negative infinity for the function (-x)/(sqr ...

Calculus - I am maybe overthinking this, but what is the lim as n-> infinity ...