TABLE OF CONTENTS If three variables x, y, z are so related that the value of z depends upon the values of x and y, then z is called a function of two variables x and y, and this is denoted by z = f( x, y).
z is called the dependent variable while x and y are called independent variables.
For example, the area of a triangle is determined when its base and altitude are known. Thus, area of a triangle is a function of two variables, base and altitude.
In a similar way, a function of more than two variables can be defined.
Geometrical Interpretation :
Let z = f( x, y) be a function of two independent variables x and y defined for all pairs of values of x and y which belong to an area A of the xy-plane. Then to each point ( x, y) of this area corresponds a value of z given by the relation z = f( x, y). Representing all these values ( x, y, z) by points in space, we get a surface.
Hence the function z = f(x, y) represents a surface.
A function f( x, y) is said to be continuous at a point ( a, b) if, for any arbitrarily chosen...
