Course Hero Logo

Chapter 14 Notes.pdf - Partial derivatives functions of...

Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. This preview shows page 1 - 3 out of 10 pages.

Partialderivativesfunctionsof severalvariables14.1supposeDisa set ofntables ofreal numbersIXX2XnArealvaluedfunctionsonDisarulethatassignsaUnionesinglereal numberWfXX2XnttoeachelementDThesetDisthe function's domainTheset ofWvaluestakenonbyf isthefunction'srangewisadependent variableoffandfissaidtobethefunctionofthenindependentvariablesxtoxn Wealsocall thexi'sthefunction's input variablesandcall w thefunction'soutputvariableclosedintervalsCabcontain boundarypointsopenintervalsaibdon'ttouchboundarypointsinteriorpointapointix gotinregionR thathasacenterofpositiveradius that liesentirelyinRboundarypointlxYocontainspointsthatliecompletelyoutsideraswell as inoron Ropenregionconsistsentirelyofinteriorpointsclosedregion containsallitsboundary pointsaregion intheplaneisboundedifit lies insideadiskoffiniteradiusAregionisunbounded ifitlacksboundarythe set ofpointsintheplane wherefxyhasaconstantvaluefxyleiscalledthelevelcurveoffthesetofallPointsXyfxyinspaceforxyin thedomainoffis calledthegraphoffThegraphoffisalsocalledthesurface2fix y
examplesgraph fixy100x2yandplot thelevelcurvesfixyo.flx.us51andjlxy75inthedomainoffin the plane2100x2y2fXy100x24207242100810fx424251rFrsobSoverheadeVysideviewsurface2100x242yExlevelsurfacetheset ofpointsix42inspace whereafunctionof3indvariableshasa constantvalueIX4,276

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 10 pages?

Upload your study docs or become a

Course Hero member to access this document

Term
Spring
Professor
Filaseta
Tags

Newly uploaded documents

Show More

Newly uploaded documents

Show More

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture