Appendix B: The Implicit Function Theorem

The equation x2+y2−1=0 describing the unit circle can be solved for y to yield the two functions y=+1−x2 (the upper half of the circle) and y=−1−x2 (the lower half). These two functions are said to be implicit in the equation x2+y2−1=0 . (The original Latin meaning of “implicit” is “folded in,” and ... View More