Is the limit below well defined ? Explain. lim x-->0 sqrt(x-x^2)

Expert Answers
lfryerda eNotes educator| Certified Educator

A limit is well-defined if and only if both the left-sided limits and the right-sided limits exist and are finite.

In this case, the right-sided limit exists and is 0, since as `x->0^+` , then the function approaches 0.

On the other hand, the left-sided limit does not exist.  The reason it does not exist is because when `x<0`

even by a little bit, then the expression `x-x^2` is negative, which means we can't take the square root.  

Since the left-sided limit does not exist, this means that the limit is not well-defined.