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- Politecnico di Milano
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- Management Engineering
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- Analisi Matematica 2
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- Exercises · By topic
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ExercisesBy topic
05 Coord Polari
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Analisi Matematica 2By topic
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dig. sin) = g- in9(e.20)= e*92(sinco)=0 e limitato 0=)sinnol=1 enitele f(ny)=0 (x,y)a(0,0) Peresercizio:Calcolore,alvaruaridiaN lin -(y+ 2)a (y)-(1,- 2)(x- 18+ (y+22 3/05/2023correzionedelmercizioassegnato am (ny)a(1,- 2)Dayteer y+2= + (x- 1)y+1= x- 1 f(t+1,t- 2)= ata=EarItax= t+1 0 a) 1y=t-8 mstheadItRa-2 - I4a=1 The a=0 esislimiteassignatorite,dueevereassociatoa questilore coordinatepolari:(x=1+9100E 2- 1= Icoso y= -2+gsindy+2= gsina un -ung2a-2asinceSorgeinco gaotI2 fasosing=(sinco)f(5,0)-gla-posasinoa 0f(9,0))= gra-zsinza*= ILa-E se 20-20aosegeneticaedeiteAa=1 &hotdedaO seun I-2=+ gaot1)siconsiderif:RRdefinitorda: fluy)- wineseener(xy)F (0,) IB (2,y)= (0,0) a)Determinareivaloridipermilafunzionesia conti nuainR2 b)perivaloridiBdeterminatialpuntoprecedente,siconsi denilafunzioneg(,y)= f(f(y),flyinl)epeoroucethe gecontinuoa tuttoR2. Caldaremaltre10,08My) a)fluy)ècontinuein R2(10,01}pencheprodottoecomposizionedifunzionicontinue affinchesiecontinuainR2deveessere: un f(xy)= f(0,0)= B(x,y)a(0,0)un - h21)an(e-81)(cy)-(0,0)rag(1+ x2y2)- [8] e- 21=- x40)si(-+ 04)= - x+0(n) eY1= - y0(y2)evi(-y0(y4))= - y*0/ylin passoincoordinate xy)alopniyy)= [8]polariIx= gcoso genosico-lettinoy=Ssine se leg(1+94= 920194 0(f(9,0)1= 3920=le3gr(sind=gt40 90tpertantoaffinchéf(x,y)siacontinuainRVdenevenBo(xy)(0,0)f(xy)- (x,y) = (0,0) b)x= f(xy)y= f(y,x)1 4xx)g(ny)= f(h(f(x,y))- grigheunfunzioneonlinePrechecomposizioneecontimee
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