prove that f(x)=sinx/x is a uniformly continous in R.
What is your difficulty? Do you know the definition of "uniformly continuous"?
(First point you need to deal with is that you cannot prove the statement as given- it isn't true! f(x)= sin(x)/x is not defined at x= 0 and so cannot be continuous there. The function "f(x)= sin(x)/x for x not equal to 0, f(0)= 1" is uniformly continuous in R.)