15-review

# 15-review - Functions of Several Variables You can use...

This preview shows pages 1–2. Sign up to view the full content.

Functions of Several Variables You can use level curves or contour curves to graph a function of 3 variables. Just set z = C , a constant. Pick several values of C and visualize the curve from these level curves. If z = C intersects z x , y , the contour curve is just a trace. Linear functions of three variables represent a plane. (Think the general plane equation.) Limits and Continuity concept behind proofs. lim x , y a , b f x , y = L iff for each 0 there is a 0 such that f x , y L whenever x , y D and 0 x x 0 2 y y 0 2 . x x 0 2 y y 0 2 defines a disc centered at x 0 , y 0 : since x and y are both variables, you can approach a point infinitely many ways, from any direction on the xy plane (thus the circle). In two dimensions, you could only approach the point two ways, from -x or +x. If you get different limits when you approach from different paths, the limit does not exist. This helps us in finding continuous functions. If you can choose 2 different paths of approach to x 0 , y 0 and they give you different limits, then the limit does not exist. This is an example of a discontinuity in three dimensions.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

15-review - Functions of Several Variables You can use...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online