Question

how do you find the limits of :

lim sinx/x where x->0

and lim 1/x-3 where x-> 3

Answer 1

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.