In considering the function , in any neighborhood of 0 has infinitely many zeros.
Therefore, because is undefined so is where is a zero of .
Because there are infinitely many places where is undefined is any neighborhood of 0, does not exist.
i would think the lim as x-->0 of f(x)/f(x) would be 1 regardless of what f(x) is. i am looking at a solution in the back of a calculus book and finding a solution of "limit doesn't exist." the function f(x) is sin(1/x). am i missing something?