Can the fundamental theorem of existence and uniqueness be applied to the initial value problem: x' = t^2/x^2, x(0) = 0? In other words, if f(t,x) = t^2/x^2, is f(t,x) and its partial derivative with respect to x continuous on some interval containing the initial conditions? My initial reaction is to say that it is not continuous since there is a zero in the denominator in both equations, however, when (0, 0) is plugged into both equations the result is 0/0. Looking at the limit as (t, x) approaches (0, 0) tells me that it is not continuous. I guess my question is, is it sufficient to just say that there is a zero in the denominator (since x(0) = 0) and the theorem cannot be applied here, or would I need to go through showing the nonexistence of the limit as (t, x) approaches (0, 0)? Thanks.