Economics 214 Lecture 4 Multivariate Functions

Linear function

Graph Linear Function

Graph function in multiple quadrants

Multivariate Function A Multivariate function has more than one argument. y=f(x 1,x 2,x 3 ) Subscripts have been used to distinguished among the different independent variables. A multivariate function with two independent variables is called a bivariate function.

Bivariate Function

Ordered Triplets

Drawing of Production Function Q K L

Plane

a {b 2 x2x2 x1x1 B1}B1} y

Limits and Continuity It is often necessary to evaluate a function as its argument approaches some value. The limit of a function as its argument approaches some number a is simply the number the function’s value approaches as the argument approaches a, either from smaller values of a, giving the left-hand limit, or from larger values of a, giving the right-hand limit.

Left-hand Limit

Right-hand Limit

Limit

Infinite Limits

Left-hand limit ≠ Right-hand limit