lim sin^2x/x

x-0

You need to use something called "L'Hopital's Rule." Basically, if a limit is indeterminate (0/0, infintiy/infinity), then L'Hopital's rule states you can take the limit of the derivative of the numerator over the derivative of the denominator. That is,

lim f(x)/g(x) = lim f'(x)/g'(x)

Have a look at the wikipedia page

http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

specifically, at the examples, and let me know if you need more help.