{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q1: " }{MPLTEXT 1 0 8 "rest art:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "y:=add(c[i]*x^i,i=0 ..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,8&%\"cG6#\"\"!\"\"\"* &&F'6#F*F*%\"xGF*F**&&F'6#\"\"#F*)F.F2F*F**&&F'6#\"\"$F*)F.F7F*F**&&F' 6#\"\"%F*)F.F " 0 "" {MPLTEXT 1 0 17 "c[0]:=1: c[1]:=2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "eq:=expand((1- x^2)*diff(y,x,x)+(x^2-2*x-5)*diff(y,x)+2*(x+2)*y);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%#eqG,jo\"\"'!\"\"*(\"\"#\"\"\"&%\"cG6#F)F*)%\"xGF)F *F'*(\"\")F*&F,6#\"\"$F*)F/F4F*F'*(\"#;F*&F,6#\"\"%F*)F/F:F*F'*(\"#EF* &F,6#\"\"&F*)F/F@F*F'*&F)F*F+F*F**&F&F*F.F*F**&F&F*F/F*F**(\"#QF*&F,6# F&F*)F/F&F*F'*(\"#_F*&F,6#\"\"(F*)F/FNF*F'*(\"#oF*&F,6#F1F*)F/F1F*F'*( \"#')F*&F,6#\"\"*F*)F/FYF*F'*(\"$1\"F*&F,6#\"#5F*)F/FinF*F'*(FinF*F+F* F/F*F'*(\"#:F*F2F*F.F*F'*(\"#?F*F8F*F5F*F'*(\"#DF*F>F*F;F*F'*(\"#IF*FG F*FAF*F'*(\"#NF*FLF*FIF*F'*(\"#SF*FRF*FOF*F'*(\"#XF*FWF*FTF*F'*(\"#]F* FgnF*FZF*F'*(F&F*F2F*F/F*F**(\"#7F*F8F*F.F*F**(F_oF*F>F*F5F*F**(FcoF*F GF*F;F*F**(\"#UF*FLF*FAF*F**(\"#cF*FRF*FIF*F**(\"#sF*FWF*FOF*F**(\"#!* F*FgnF*FTF*F**(F:F*F5F*F+F*F**(F@F*F;F*F2F*F**(F&F*FAF*F8F*F**(FNF*FIF *F>F*F**(F1F*FOF*FGF*F**(FYF*FTF*FLF*F**(FinF*FZF*FRF*F**(\"#6F*FjnF*F WF*F**(F^pF*)F/FaqF*FgnF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "solve(\{eval(eq,x=0),seq(coeff(eq,x,i),i=1..8)\},\{seq(c[i],i=2..1 0)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<+/&%\"cG6#\"\"#\"\"$/&F&6# \"\"%\"\"&/&F&6#F.\"\"'/&F&6#\"\"(\"\")/&F&6#\"\"*\"#5/&F&6#F<\"#6/&F& 6#F7F;/&F&6#F2F6/&F&6#F)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "sum((i+1)*x^i,i=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#* &\"\"\"F$*$),&%\"xGF$F$!\"\"\"\"#F$F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q2:" }{MPLTEXT 1 0 22 " restart:with(linalg):" }}{PARA 7 " " 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have b een redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A:=matrix(3,3,[3,3,2,-1,-3,3,-1,4,-4]):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 31 "solve(x^3+4*x^2-16*x-det(A),x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6%!\"(,&#\"\"$\"\"#\"\"\"*&^##F(F'F(\"#6F+F(,&F%F( *&^##!\"\"F'F(F,F+F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gau ssjord(A+7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"\" \"\"!#!\"\"\"#V7%F)F(#\"#KF,7%F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "q1:=[1,-32,43]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#q1G7%\"\"\"!#K\"#V" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "gau ssjord(A-3/2-sqrt(11)*I/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matr ixG6#7%7%\"\"\"\"\"!,&#\"\"$\"\"#F(*&^##F(F-F(\"#6F0F(7%F)F(!\"\"7%F)F )F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "q2:=[3/2+sqrt(11)*I/ 2,-1,-1]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "y1:=evalm(q1*e xp(-7*x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%'vectorG6#7%-%$e xpG6#,$*&\"\"(\"\"\"%\"xGF/!\"\",$*&\"#KF/F)F/F1,$*&\"#VF/F)F/F/" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "assume(x,real):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "y2:=[seq(Re(q2[i]*exp(3/2*x+sqrt(11 )*I/2*x)),i=1..3)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "y3:= [seq(Im(q2[i]*exp(3/2*x+sqrt(11)*I/2*x)),i=1..3)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "linsolve(eval(augment(y1,y2,y3),x=0),[3/2,- 1,-1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"\"!\"\"\"F' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "y2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,&*&#\"\"$\"\"#\"\"\"*&-%$expG6#,$*(F'F)F(!\"\"%#x|ir GF)F)F)-%$cosG6#,$*(F(F0\"#6#F)F(F1F)F)F)F)F)*&#F)F(F)*(F7F8F+F)-%$sin GF4F)F)F0,$F*F0F>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q3:" } {MPLTEXT 1 0 10 " restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "solve(m*(m-1)*(m-2)*(m-3)+8*m*(m-1)*(m-2)+m*(m-1)-49*m-32,m);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"%!\"#F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "yh:=A*x^4+B/x^2+C/x^2*ln(x)+D/x^2*ln(x)^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yhG,**&%\"AG\"\"\")%\"xG\"\"%F(F(*& %\"BGF(F*!\"#F(*(%\"CGF(F*F.-%#lnG6#F*F(F(*(%\"DGF(F*F.F1\"\"#F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "yp:=x^2*(a*ln(x)+b):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "simplify(x^4*diff(yp,x,x,x, x)+8*x^3*diff(yp,x,x,x)+x^2*diff(yp,x,x)\n-49*x*diff(yp,x)-32*yp-x^2*l n(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&)%\"xG\"\"#\"\"\",**&\"# KF(%\"aGF(F(*(\"$G\"F(F,F(-%#lnG6#F&F(F(*&F.F(%\"bGF(F(F/F(F(!\"\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "a:=-1/128: b:=-32*a/128: \+ yp;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG\"\"#\"\"\",&*&#F'\"$ G\"F'-%#lnG6#F%F'!\"\"#F'\"$7&F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q4:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "eq:=4*x^2* diff(y(x),x,x)+12*x*diff(y(x),x)+(4*x-5)*y(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG,(*(\"\"%\"\"\")%\"xG\"\"#F(-%%diffG6$-%\"yG6#F*- %\"$G6$F*F+F(F(*(\"#7F(F*F(-F-6$F/F*F(F(*&,&*&F'F(F*F(F(\"\"&!\"\"F(F/ F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eq1:=expand(eval(eq ,y(x)=u(x)/x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,**(\"\"%\" \"\"%\"xGF(-%%diffG6$-%\"uG6#F)-%\"$G6$F)\"\"#F(F(*&F'F(-F+6$F-F)F(F(* (\"\"*F(F-F(F)!\"\"F9*&F'F(F-F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Z:=2*sqrt(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "eq2:=expand(4*x^2*(diff(u(z),z,z)*diff(Z,x)^2+diff(u(z),z)*di ff(Z,x,x))\n+4*x*diff(u(z),z)*diff(Z,x)-(9-4*x)*u(z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G,**(\"\"%\"\"\"%\"xGF(-%%diffG6$-%\"uG6#%\" zG-%\"$G6$F0\"\"#F(F(*(F4F(F)#F(F4-F+6$F-F0F(F(*&\"\"*F(F-F(!\"\"*(F'F (F-F(F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "eq2:=expand( eval(eq2,\{sqrt(x)=z/2,x=z^2/4\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$eq2G,**&)%\"zG\"\"#\"\"\"-%%diffG6$-%\"uG6#F(-%\"$G6$F(F)F*F**&F(F *-F,6$F.F(F*F**&\"\"*F*F.F*!\"\"*&F.F*F'F*F*" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 42 "Bessel, n = 3: u = A.J3(z) + B.Y3(z)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "y(x):=(A*BesselJ (3,2*sqrt(x))+B*BesselY(3,2*sqrt(x)))/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"yG6#%\"xG*&,&*&%\"AG\"\"\"-%(BesselJG6$\"\"$,$*&\"\"#F,F'#F ,F3F,F,F,*&%\"BGF,-%(BesselYGF/F,F,F,F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q5:" }{MPLTEXT 1 0 10 " \+ restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dot:=proc(r,q) ;simplify(add(r[i]*q[i],i=1..3)) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "mag:=proc(q);sqrt(add(q[i]^2,i=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plugin:=proc(g,r);eval(g,\{x=r[1],y =r[2],z=r[3]\})end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "cros s:=proc(r,q);[r[2]*q[3]-r[3]*q[2],r[3]*q[1]-r[1]*q[3],r[1]*q[2]-r[2]*q [1]] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "curl:=proc(g); [diff(g[3],y)-diff(g[2],z),diff(g[1],z)-diff(g[3],x),diff(g[2],x)-diff (g[1],y)]end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g:=[x^2,x* y,3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG7%*$)%\"xG\"\"#\"\"\"*& F(F*%\"yGF*\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "r:=[-1+ 3*cos(t),2+3*sin(t),-3]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "int(dot(plugin(g,r),diff(r,t)),t=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"#=\"\"\"%#PiGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "r:=[-1+v*cos(u),2+v*sin(u),-3]: aux:=cross(diff(r,u) ,diff(r,v)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "int(int(dot (plugin(curl(g),r),aux),u=0..2*Pi),v=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"#=\"\"\"%#PiGF&!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q6:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "r1:=[2*sin(v)*cos(u),2*sin(v)*sin(u),2*cos(v)]:\naux: =simplify(cross(diff(r1,u),diff(r1,v)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG7%,$*(\"\"%\"\"\",&F)!\"\"*$)-%$cosG6#%\"vG\"\"#F)F)F)-F/ 6#%\"uGF)F),$*(F(F)F*F)-%$sinGF4F)F),$*(F(F)-F9F0F)F.F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "-int(int(dot(plugin(g,r1),aux),u=0. .2*Pi),v=0..Pi/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"#7\"\"\"%# PiGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "r2:=[v*cos(u),v* sin(u),0]:\naux:=simplify(cross(diff(r2,u),diff(r2,v)));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "int(int(dot(plugin(g,r2),aux),u=0..2*Pi),v=0. .2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG7%\"\"!F&,$%\"vG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"#7\"\"\"%#PiGF&!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "int(3*x,z=0..sqrt(4-x^2-y^2) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"$\"\"\"%\"xGF&,(\"\"%F&* $)F'\"\"#F&!\"\"*$)%\"yGF,F&F-#F&F,F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "int(int(3*rho*cos(theta)*sqrt(4-rho^2)*rho,theta=0..2 *Pi),rho=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q7:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "z:=(2-3*I)+(-4+6*I)*t: int(z^2/abs(z-I)^3 *diff(z,t),t=0..1.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+]^=-s!\" *$\"+#=B\"49F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q8:" }{MPLTEXT 1 0 10 " restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "s:=so lve(z^4+I*z^2+2,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6&,&*&\" \"#!\"\"F(#\"\"\"F(F+*&^#F*F+F(F*F+,&*&F(F)F(F*F)*&^##F)F(F+F(F*F+^$F) F+^$F+F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "seq(evalf(abs(s [i]-I/2)),i=1..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&$\"+!zG\"ot!#5$ \"+Ej'*)R\"!\"*$\"+))R.=6F($\"+Qcx-=F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "residue(z^2/(z^4+I*z^2+2),z=(1+I)/sqrt(2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*&^#\"\"$\"\"\"\"\"##F(F)F(*&F'F(F)F*!\" \"F,^#F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalc(2*Pi*I* %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"'!\"\"%#PiG\"\"\"\"\"## F(F)F(*(^##F(F%F(F'F(F)F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+)*[![S(!#5F$" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q9:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "s:=solve(x^4+x^2+3,x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&^$$!+&eG([y!#5$!+N5Uc5!\"*^$$\"+&eG([yF&$\"+N5Uc5F)^$F$ F-^$F+F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "residue(x^2/(x^ 4+x^2+3),x=s[2])+residue(x^2/(x^4+x^2+3),x=s[3]):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"#A!\"\",**(,&\"\"#F&*&^#!\"#\"\"\"\"#6#F.F*F.F0F/F0^#F.F.F .*&F/F.F)F0F.*(,&F*F&*&^#F*F.F/F0F.F0F/F0F1F.F.*&F/F.F4F0F&F.F4#F&F*F) F8F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "simplify(evalc(Pi*% *I)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*,\"$K\"!\"\"%#PiG\"\"\",& *&\"\"#F(\"\"$#F(F+F(F(F&F-\"#6F-F,F-F&**\"#7F&F'F(,&*&F+F(F,F-F(F(F(F -F,F-F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+8%=XV(!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q10:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "r:=[3*cos(t),sin(t),1+sin(t)^2]:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 51 "dot:=proc(r,q);simplify(add(r[i]*q[i],i=1..3 )) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "v:=diff(r,t): a :=diff(v,t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "eval(sqrt(( dot(v,v)*dot(a,a)-dot(v,a)^2)/(dot(v,v)^3)),t=0):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"+v7b0O!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "cross:=pro c(r,q);[r[2]*q[3]-r[3]*q[2],r[3]*q[1]-r[1]*q[3],r[1]*q[2]-r[2]*q[1]] e nd:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "eval(dot(v,cross(a,d iff(a,t)))/(dot(v,v)*dot(a,a)-dot(v,a)^2),t=0):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"\"!F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q11:" }{MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(1,z=x^2+y^2..4);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"%\"\"\"*$)%\"xG\"\"#F%!\"\"*$)% \"yGF)F%F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "A:=2*Pi*int(( 4-rho^2)*rho,rho=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,$*& \"\")\"\"\"%#PiGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "fac tor(int(x^2+y^2,z=x^2+y^2..4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$* &,&*$)%\"xG\"\"#\"\"\"F**$)%\"yGF)F*F*F*,(F&F*\"\"%!\"\"F+F*F*F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "M/A*2*Pi*int(rho^3*(4-rho^2) ,rho=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"%\"\"\"\"\"$!\" \"%\"MGF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q12:" }{MPLTEXT 1 0 11 " restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "r:=[v* cos(u),v*sin(u),v^2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ma g:=proc(q);sqrt(add(q[i]^2,i=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "cross:=proc(r,q);[r[2]*q[3]-r[3]*q[2],r[3]*q[1]-r[1]* q[3],r[1]*q[2]-r[2]*q[1]] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "aux:=simplify(mag(cross(diff(r,u),diff(r,v))));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$auxG*$*&)%\"vG\"\"#\"\"\",&*&\"\"%F*F'F*F*F*F *F*#F*F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A:=int(aux,v=0. .2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,&*(\"#<\"\"\"\"#7!\"\"F '#F(\"\"#F(#F(F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "[0,0, evalf(int(v^2*aux,v=0..2)/A)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\" \"!F$$\"+$*etMB!\"*" }}}}{MARK "25 0 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }