ISM_T11_C14_A - CHAPTER 14 PARTIAL DERIVATIVES 14.1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CHAPTER 14 PARTIAL DERIVATIVES 14.1 FUNCTIONS OF SEVERAL VARIABLES 1. (a) Domain: all points in the xy-plane (b) Range: all real numbers (c) level curves are straight lines y x c parallel to the line y x ±œ œ (d) no boundary points (e) both open and closed (f) unbounded 2. (a) Domain: set of all (x y) so that y x 0 y x ß±   Ê   (b) Range: z 0   (c) level curves are straight lines of the form y x c where c 0   (d) boundary is y x 0 y x, a straight line È ±œ Ê œ (e) closed (f) unbounded 3. (a) Domain: all points in the xy-plane (b) Range: z 0   (c) level curves: for f(x y) 0, the origin; for f(x y) c 0, ellipses with center ( 0) and major and minor ßœ ßœ² ! ß axes along the x- and y-axes, respectively (d) no boundary points (e) both open and closed (f) unbounded 4. (a) Domain: all points in the xy-plane (b) Range: all real numbers (c) level curves: for f(x y) 0, the union of the lines y x; for f(x y) c 0, hyperbolas centered at œ ßœÁ (0 0) with foci on the x-axis if c 0 and on the y-axis if c 0 ß² ³ (d) no boundary points (e) both open and closed (f) unbounded 5. (a) Domain: all points in the xy-plane (b) Range: all real numbers (c) level curves are hyperbolas with the x- and y-axes as asymptotes when f(x y) 0, and the x- and y-axes ßÁ when f(x y) 0 (d) no boundary points (e) both open and closed (f) unbounded 6. (a) Domain: all (x y) (0 y) ßÁß (b) Range: all real numbers (c) level curves: for f(x y) 0, the x-axis minus the origin; for f(x y) c 0, the parabolas y cx minus the œ # origin (d) boundary is the line x 0 œ
Background image of page 1

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

View Full DocumentRight Arrow Icon
864 Chapter 14 Partial Derivatives (e) open (f) unbounded 7. (a) Domain: all (x y) satisfying x y 16 ß± ² ## (b) Range: z   " 4 (c) level curves are circles centered at the origin with radii r 4 ² (d) boundary is the circle x y 16 ±œ (e) open (f) bounded 8. (a) Domain: all (x y) satisfying x y 9 Ÿ (b) Range: 0 z 3 ŸŸ (c) level curves are circles centered at the origin with radii r 3 Ÿ (d) boundary is the circle x y 9 (e) closed (f) bounded 9. (a) Domain: (x y) (0 0) ßÁß (b) Range: all real numbers (c) level curves are circles with center ( 0) and radii r 0 ³ (d) boundary is the single point (0 0) ß
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

ISM_T11_C14_A - CHAPTER 14 PARTIAL DERIVATIVES 14.1...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online