<Text-field style="Heading 1" layout="Heading 1">Question 1: Calcul d'aire entre deux courbes. Page 167 # 9 h)</Text-field>
restart:with(plottools):with(plots):Digits:=5:with(RealDomain):
f:=x->1/(x+1) ; g:=x-> x/(x^2+1);
Sfg:=solve(f(x)=g(x));
a:=plot([g(x),f(x)],x=-5..10,thickness=[3,4],numpoints=1000,color=[red,green,blue]):
b:=textplot([-0.5,f(-0.5)-0.5,`f`],align=RIGHT):
c:=textplot([-0.5,g(-0.5)-0.2,`g`],align=RIGHT):
e:=plot([g(x),f(x)],x=0..Sfg,filled=true,color=[white,yellow]):
r1:=rectangle([.2,g(.2)],[.23,f(.2)],color=gray):
display([r1,e,a,b,c],view=[-0.7..1.2,-1..2]);
A:= Int(f(x)-g(x),x=0..Sfg)=int(f(x)-g(x),x=0..Sfg)*u^2 ;
A:=evalf(rhs(%));
<Text-field style="Heading 1" layout="Heading 1"> Question 2: Calcul d'un volume avec une rotation autour de l'axe des y. Page 274 # 2d)</Text-field>
restart: with(plots): Digits:=5:readlib(isolate):with(plottools):
f:=x->cos(x);
C:=plot(f(x),x=-Pi..3*Pi/2):
d1:=plot(f(x),x=0..Pi,filled=true,color=magenta):
r1:=rectangle([1,0],[1.2,f(1)],color=green):
d:=textplot([1.2,f(1.2)+.4,`f`]):
r2:=rectangle([2.5,0],[2.7,f(2.5)],color=green):
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
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJXBsb3RGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2LS1GUzYmLUYjNi4tRiw2JVEjUGlGJy9GMEY9RjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGL0YyRmluRmFvLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZbcC1JI21uR0YkNiRRJDEuMUYnRjktRjY2LVEjLi5GJ0Y5RjtGPkZARkJGREZGRkhGam8vRk5GXm8tRl5wNiRRJDEuMkYnRjkvJStleGVjdXRhYmxlR0Y9RjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zpbi1GLDYlUSZjb2xvckYnRi9GMkZkby1GLDYlUSZncmVlbkYnRmhuRjlGaW4tRiw2JVEqdGhpY2tuZXNzRidGL0YyRmRvLUZTNiYtRiM2Jy1GXnA2JFEiM0YnRjlGaW4tRl5wNiRRIjRGJ0Y5RmhwRjlGOUZqcEZdcUZocEY5RjktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GaHBGOQ==
display(a,b,r1,r2,d,d1,C,view=[-Pi..3*Pi/2,-1.2..1.2],labels=[x,y]);
with(plots): with(plottools):
a:=0: b:=Pi: c:=0:
axe:=plot3d([c,y,0],y=0..1.2, t=0..2):
C1:=plot3d([(x-c)*sin(t)+c,f(x),(x-c)*cos(t)],x=a..b,t=0..1*Pi): C2:=plot3d([Pi*sin(t)+c,y,Pi*cos(t)],y=-1..0,t=0..1*Pi,style = WIREFRAME):
C3:=plot3d([(x-c)*sin(t)+c,0,(x-c)*cos(t)],x=a..b,t=0..1*Pi,color=blue):
display(axe, C1,C2,C3,axes=normal, labels=[X,Y,Z],orientation=[-90,-20]);
par la m\303\251thode des tubes
r:=x;
h:=f(x);
Int(2*Pi*r*h,x=0..Pi/2)+Int(2*Pi*r*(-h),x=Pi/2..Pi)=(int(2*Pi*r*h,x=0..evalf(Pi/2))+int(2*Pi*r*(-h),x=evalf(Pi/2)..Pi))*u^3;
<Text-field style="Heading 1" layout="Heading 1">Question 4: Calcul d'une aire de surface. Page 275 # 11 c)</Text-field>
restart:with(plots):with(plottools):with(student):
Digits:=6;
x:=t->25*cos(t);
y:=t->25*sin(t);
a:=arcsin(10./25);
b:=Pi-arcsin(10./25);
c:=plot([x(t),y(t),t=a..b],scaling=CONSTRAINED):
display(c,view=[-25..25,0..25]);
x:=y->sqrt(25^2-y^2);
with(plots): with(plottools):
a:=10: b:=25: c:=0:
axe:=plot3d([c, s, 0], s=-0.4..28, t=0..28):
C1:=plot3d([ x(y-c)*sin(t)+c,y,x(y-c)*cos(t)],y=10..25,t=0..2*Pi):
display(axe, C1, axes=normal, labels=[X,Y,Z],scaling=constrained,orientation=[90,180]);
r:=x(y);
S:=Int(2*Pi*r*sqrt(1+(diff(x(y),y))^2),y=10..25)=int(2*Pi*r*sqrt(1+(diff(x(y),y))^2),y=10..25);
s:=evalf(rhs(%));
couts:=s*.6*dollars;
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1JI21vR0YkNi1RIn5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkYvJSlzdHJldGNoeUdGRi8lKnN5bW1ldHJpY0dGRi8lKGxhcmdlb3BHRkYvJS5tb3ZhYmxlbGltaXRzR0ZGLyUnYWNjZW50R0ZGLyUnbHNwYWNlR0Y3LyUncnNwYWNlR0Y3Ri8tRjA2JkYyRjVGOC9GO1ElYXV0b0YnRisvJStleGVjdXRhYmxlR0ZGRkE=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 1: C\303\241lculo da \303\241rea entre duas curvas. P\303\241gina 167 # 9 h)</Font></Text-field>
restart:with(plottools):with(plots):Digitos:=5:with(RealDomain):
f:=x->1/(x+1) ; g:=x-> x/(x^2+1);
Sfg:=solve(f(x)=g(x));
a:=plot([g(x),f(x)],x=-5..10,thickness=[3,4],numpoints=1000,color=[red,green,blue]):
b:=textplot([-0.5,f(-0.5)-0.5,`f`],align=RIGHT):
c:=textplot([-0.5,g(-0.5)-0.2,`g`],align=RIGHT):
e:=plot([g(x),f(x)],x=0..Sfg,filled=true,color=[white,yellow]):
r1:=rectangle([.2,g(.2)],[.23,f(.2)],color=gray):
display([r1,e,a,b,c],view=[-0.7..1.2,-1..2]);
A:= Int(f(x)-g(x),x=0..Sfg)=int(f(x)-g(x),x=0..Sfg)*u^2 ;
A:=evalf(rhs(%));
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRidGKy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> Quest\303\243o 2: C\303\241lculo de um volume com rota\303\247\303\243o em torno do eixo y. P\303\241gina 274 # 2d)</Font></Text-field>
restart: with(plots): Digitos:=5:readlib(isolate):with(plottools):
f:=x->cos(x);
C:=plot(f(x),x=-Pi..3*Pi/2):
d1:=plot(f(x),x=0..Pi,filled=true,color=magenta):
r1:=rectangle([1,0],[1.2,f(1)],color=green):
d:=textplot([1.2,f(1.2)+.4,`f`]):
r2:=rectangle([2.5,0],[2.7,f(2.5)],color=green):
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
display(a,b,r1,r2,d,d1,C,view=[-Pi..3*Pi/2,-1.2..1.2],labels=[x,y]);
with(plots): with(plottools):
a:=0: b:=Pi: c:=0:
axe:=plot3d([c,y,0],y=0..1.2, t=0..2):
C1:=plot3d([(x-c)*sin(t)+c,f(x),(x-c)*cos(t)],x=a..b,t=0..1*Pi): C2:=plot3d([Pi*sin(t)+c,y,Pi*cos(t)],y=-1..0,t=0..1*Pi,style = WIREFRAME):
C3:=plot3d([(x-c)*sin(t)+c,0,(x-c)*cos(t)],x=a..b,t=0..1*Pi,color=blue):
display(axe, C1,C2,C3,axes=normal, labels=[X,Y,Z],orientation=[-90,-20]);
pelo m\303\251todo do tubo
r:=x;
h:=f(x);
Int(2*Pi*r*h,x=0..Pi/2)+Int(2*Pi*r*(-h),x=Pi/2..Pi)=(int(2*Pi*r*h,x=0..evalf(Pi/2))+int(2*Pi*r*(-h),x=evalf(Pi/2)..Pi))*u^3;
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRidGKy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==JSFH
JSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 4: C\303\241lculo de uma \303\241rea de superf\303\255cie. P\303\241gina</Font> 275 # 11 c)</Text-field>
restart:with(plots):with(plottools):with(student):
Digitos:=6;
x:=t->25*cos(t);
y:=t->25*sin(t);
a:=arcsin(10./25);
b:=Pi-arcsin(10./25);
c:=plot([x(t),y(t),t=a..b],scaling=CONSTRAINED):
display(c,view=[-25..25,0..25]);
x:=y->sqrt(25^2-y^2);
with(plots): with(plottools):
a:=10: b:=25: c:=0:
axe:=plot3d([c, s, 0], s=-0.4..28, t=0..28):
C1:=plot3d([ x(y-c)*sin(t)+c,y,x(y-c)*cos(t)],y=10..25,t=0..2*Pi):
display(axe, C1, axes=normal, labels=[X,Y,Z],scaling=constrained,orientation=[90,180]);
r:=x(y);
S:=Int(2*Pi*r*sqrt(1+(diff(x(y),y))^2),y=10..25)=int(2*Pi*r*sqrt(1+(diff(x(y),y))^2),y=10..25);
s:=evalf(rhs(%));
custos:=s*.6*dollars;
JSFH
JSFH
JSFH