Question

help! :( (see attachment)

Answer 1

x*(9 - x - x³)
-------------
x* ( x² + 12)

9 - x - x²
----------
x² +12

x* ( 9/x - 1 - x)
----------------
x * ( x + 12/x)

-1 - x
------
x

-x / x - 1/x = -1 - 1/x = -1 - infinity = infinity

Answer 2

you could also divide every term by x^3
Note: lim a/x^n = 0 as x->infinity

Answer 3

just look at the degree of the top and the degree of the bottom...
if the degree on the top is more than the bottom, no limit
if the degree are equal, limit is the ratio of the coefficients
if the degree on the top is less than the degree on the bottom, limit is zero

Answer 4

ok honestly I could do this, i just want to make sure i got it right. my answer cam out to be -7.

Answer 5

no degree on top is higher, so there is no real limit
it should be either +- infinity
in this case since coefficient of x^4 is negative, limit is -infinity

Answer 6

can it be Does not exist?