Limity

> restart;

> with(plots):

> pom:=z=(x^2+y^2-2*x-2*y)/(x^2+y^2-2*x+2*y+2):

zadani fce f(x,y)

> f:=(x,y)->(x^2+y^2-2*x-2*y)/(x^2+y^2-2*x+2*y+2);

sekvence bodu, ktere jsou pruseciky fce(x,y) s rovinou z=40..220 v bode o souradnici y=-1

> bb:=[{solve(eval(eval(pom,z=20),y=-1),x)},{solve(eval(eval(pom,z=40),y=-1),x)},{solve(eval(eval(pom,z=60),y=-1),x)},{solve(eval(eval(pom,z=80),y=-1),x)},{solve(eval(eval(pom,z=100),y=-1),x)},{solve(eval(eval(pom,z=120),y=-1),x)},{solve(eval(eval(pom,z=140),y=-1),x)},{solve(eval(eval(pom,z=160),y=-1),x)},{solve(eval(eval(pom,z=180),y=-1),x)},{solve(eval(eval(pom,z=200),y=-1),x)},{solve(eval(eval(pom,z=220),y=-1),x)}];

zobrazeni techto bodu

> bbod:=[

> pointplot3d({[bb[1][2],-1,20]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[2][2],-1,40]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[3][1],-1,60]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[4][1],-1,80]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[5][2],-1,100]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[6][2],-1,120]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[7][2],-1,140]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[8][2],-1,160]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[9][2],-1,180]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[10][2],-1,200]},symbolsize=30,symbol=circle,color=red),

> pointplot3d({[bb[11][1],-1,220]},symbolsize=30,symbol=circle,color=red)

> ]:

> body:=display(bbod,insequence=true,view=[0.5..1.5,-1.7..-0.5,-1..200],axes=BOXED):

zobrazeni fce f(x,y)

> fce:=plot3d(f(x,y), x=0.5..1.5,y=-1.7..-0.5,view=-1..200,style=patchcontour,grid=[50,50], axes=box, tickmarks=[5,6,2]):

pomocna limita

> Limit(f(x,y),x=1)=infinity;

> display(body,fce, orientation=[156,67]);

>