Can you help me find the limit and its horizontal asymptote(Calculus - Limits)?

Question

a)
find lim x---> +infinity of f(x)
b)
find lim x---> -infinity of f(x)
c)
identify all horizontal asymptotes

all this without using a calculator?

Well the equation is

3(x^3) - x + 1
----------------- divided by
x+3

So, how are we suppose to do this without using a calculator. What exactly does x --> infinity / -infinity mean?

Most importantly, how the heck do we find the horizontal asymptotes of such equation?

*this is not homework, studying for my test*

santman - THANKS but we are looking for HORIZONTAL not VERTICAL asymptotes

Answer 1

http://www.purplemath.com/modules/asymtote2.htm

this may help, I'm in the same situation

Answer 2

= (3x^2-1+1/x)/(1+3/x) ( dividing up and down by x)
3x^2==> to +infinity both for x==> +- infinity
-1+1/x tends to-1 and the denominator tends to 1
so the limit is + infinity.So there is no horizontal asymptote
There is a vertical asymptote X=-3

Answer 3

lim x?? [ (4x^3 - 4x^2 - 7x) / (8 - 8x - 3x^3) ] = lim x?? [ (4x^3 - 4x^2 - 7x) / (-3x^3 - 8x + 8) ] = lim x?? [ (a million / x^3)(4x^3 - 4x^2 - 7x) / (a million / x^3)(-3x^3 - 8x + 8) ] = lim x?? [ (4 - (4 / x) - (7 / x^2)) / (-3 - (8 / x^2) + (8 / x^3)) ] = (4 - (4 / ?) - (7 / ?^2)) / (-3 - (8 / ?^2) + (8 / ?^3)) = (4 - 0 - (7 / ?)) / (-3 - (8 / ?) + (8 / ?)) = (4 - 0) / (-3 - 0 + 0) = 4 / -3 = -4 / 3 if f(x) and g(x) are polynomials, and q and p are the coefficients of the words of utmost degree of f(x) and g(x) respectively, then, lim x?? [ f(x) / g(x) ] = 0 , if g(x) is of better degree than f(x) lim x?? [ f(x) / g(x) ] = ? , if f(x) is of better degree than g(x) lim x?? [ f(x) / g(x) ] = q/p , if f(x) and g(x) are of the comparable degree 2. lim x?? [ (6x^3 - 8x^2 - 10x) / (6 - 10x - 5x^3) ] = 6 / -5 = -6 / 5