# week05 - Math 23 Sections 110-113 B Dodson Week 5 Homework...

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

Unformatted text preview: Math 23 Sections 110-113 B. Dodson Week 5 Homework: 14.1 graphs, level curves/surfaces, contour maps 14.2 limits 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). 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 non-negative input, so we must restrict ( x, y, z ) so that z- x 2- y 2 is non-negative. 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 3-space 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 } . 2 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

week05 - Math 23 Sections 110-113 B Dodson Week 5 Homework...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online