Limits

Limits of Polynomials are one of the easiest things of Math Analysis EVER! All you have to do is plug in the number!
For instance

lim 2x+1
x -> 4
 = 2(4) + 1
 = 9
WINNER WINNER CHICKEN DINNER

Limits of Rational Functions are a little big more difficult, because they usually equal 0/0 which means they are intermediate!
When this occurs, you must do cancellation. This is when you factor your given function, cancel out terms, and then plug in your x again.

lim        x-1/(x-1)(x+1)
x-> 1
 = cancel out x - 1
 plug 1 in for x
 = 1/2