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picture1_Worksheet 120313 Alt Sol


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 80x       Filetype PDF       File size 0.60 MB       Source: faculty.math.illinois.edu


File: Worksheet 120313 Alt Sol
Tuesday,December3 ∗ Solutions ∗ Surfaceintegralsofvectoreldsandrelatedtheorems 1. ConsidertheregionD inR3 boundedbythexy-planeandthesurfacex2+y2+z=1. (a) MakeasketchofD. Solution. ThesketchofD isshownbelow. (b) TheboundaryofD,denoted∂D,hastwoparts: thecurvedtopS1 andtheatbottomS2. ParameterizeS1andcalculatetheuxofF=(0,0,z)throughS1withrespecttotheupward pointingunitnormalvectoreld. Checkyouanswerwiththeinstructor. Solution. ToparametrizeS1,onehas ...

icon picture PDF Filetype PDF | Posted on 26 Jan 2023 | 2 years ago

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...Tuesday december solutions surfaceintegralsofvectoreldsandrelatedtheorems considertheregiond inr boundedbythexy planeandthesurfacex y z a makeasketchofd solution thesketchofd isshownbelow b theboundaryofd denoted d hastwoparts thecurvedtops andtheatbottoms parameterizesandcalculatetheuxoff throughswithrespecttotheupward pointingunitnormalvectoreld checkyouanswerwiththeinstructor toparametrizes onehas r u v ucosv usinv inordertocalculatetheux rstwehave ru cosv sinv rv andso therefore theuxoff throughs withrespecttotheupwardpointingunitnor malvectoreldis isf nds zf dudv c withoutdoingthefullcalculation determinetheuxoffthroughs withthedownward pointingnormals sincef ons weknowtheuxoffthroughsis i f s determinetheuxoffthrough withtheoutwardpointingnormals byaddinguptheresultfrom and onegets e applythedivergencetheoremandyouranswerin tondthevolumeofd checkyour answerwiththeinstructor bythedivergencetheorem df nddivfdv sincedivf volume n dv divfdv considerthevectoreldf x computecurlf j k cu...
								

							

						
	
												
				
					
					
					
			
					
				
				
		
	

	
		





	

	
				

						

						
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										Category:  Uncategorized / Uncategorized 
										
Posted on: 26 Jan 2023 | 2 years ago
										
										
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																								120313,
											                                        
																				
Filetype: PDF
										
File size: 0.60 MB
										
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												Wan learn