Define Jacobian of implicit functions.
Answers
Answer:
Step-by-step explanation:
Implicit functions. Let y be related to x by the equation
(1) f(x, y) = 0
and suppose the locus is that shown in Figure 1. We cannot say that y is a function of x since at a particular value of x there is more than one value of y (because, in the figure, a line perpendicular to the x axis intersects the locus at more than one point) and a function is, by definition, single-valued. Although equation (1) above does not define y as a function of x, we can say that on certain judiciously chosen segments of the locus y can be considered to be a single-valued function of x [expressible as y = f(x)]. For example, the segment P1P2 could be separated out as defining a function y = f(x). As a consequence, it is customary to say that equation (1) defines y implicitly as a function of x; and we refer to y as an implicit function of x.
