1> lim ((3x^3)-2x) / ((x^2)-1)
x->infinite
2> lim 1/ |x-3|
x->3-
Look at the highest power of the numerator versus the denominator. The numerator has a degree of 3 while the denominator has a degree of two. You should see that as as grows larger and larger, the top far outgrows the bottom and this limit is infinity.
You should first realize that this is a form of the rational graph shifted to the right 3 units, and all negative values are flipped about the x-axis. Here's how I would do this problem. Test the value -2.9. How big is that number? Is it positive or negative? Now test -2.99, then -2.9999. See the trend?