1. Economics 214 Lecture 4 Multivariate Functions

2. Linear function

3. Graph Linear Function

4. Graph function in multiple quadrants

5. 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.

6. Bivariate Function

7. Ordered Triplets

8. Drawing of Production Function Q K L

9. Plane

10. a {b 2 x2x2 x1x1 B1}B1} y

11. 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.

12. Left-hand Limit

13. Right-hand Limit

14. Limit

15. Infinite Limits

16. Left-hand limit ≠ Right-hand limit