how do you find the limits of :
lim sinx/x where x->0
and lim 1/x-3 where x-> 3
Here is a Youtube presentation of the Proof, done by Khan, who has a whole bunch of these presentations.
lim sinx/x = 1
x-->0
http://www.youtube.com/watch?v=Ve99biD1KtA
For your second, it should be intuitively obvious that as x ---> 3, the x-3 ---> 0
and you would be dividing by zero.
so the limit 1/(x-3) as x -->3 is undefined.