This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 23 B. Dodson Week 5: functions of several variables 14.1 graphs, level curves/surfaces, contour maps 14.2 limits 14.3 Partial Derivatives Problem 14.1.9b: Find the domain of f ( x, y, z ) = e √ z x 2 y 2 . Solution: By definition, the domain of a function defined by a formula is the collection of points for which the formula makes sense (rather than by specifiying a particular subset). 2 We analyze the formula in pieces (as a composite of functions). For the exponential function, e w is defined for all w , so this gives no restriction. Next, the squareroot is only defined on nonnegative input, so we must restrict ( x, y, z ) so that z x 2 y 2 is nonnegative. We check the boundary points, ones for which 0 = z x 2 y 2 , or z = x 2 + y 2 ; which we recognize as an elliptic paraboloid. This boundary surface divides 3space into two regions, and we see z x 2 y 2 positive on the region above the paraboloid, so domain( f ) = { ( x, y, z ) so z ≥ x 2 + y 2 } ....
View
Full
Document
This note was uploaded on 03/26/2010 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .
 Spring '06
 YUKICH
 Calculus, Derivative, Limits

Click to edit the document details