{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {CSTYLE "" -1 256 "Times New Roman CE" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "H eading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } 1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 4 "" 0 "" {TEXT 256 10 "P\370\355klad 6." }{TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 47 "Vypo \350\355tejte obsah mno\236iny ohrani\350en\351 k\370ivkami " } {XPPEDIT 18 0 "y=sin(x)" "6#/%\"yG-%$sinG6#%\"xG" }{TEXT 258 3 " , " } {XPPEDIT 18 0 "y=cos(x)" "6#/%\"yG-%$cosG6#%\"xG" }{TEXT 262 3 " , " } {XPPEDIT 18 0 "x=0" "6#/%\"xG\"\"!" }{TEXT 263 5 " a " }{XPPEDIT 18 0 "x=Pi/2" "6#/%\"xG*&%#PiG\"\"\"\"\"#!\"\"" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT 259 1 " " }}{EXCHG {PARA 0 "" 0 "" {TEXT 261 36 "nadef inujeme funkce sinus a kosinus " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " f1 := x -> sin(x); f2 := x -> cos(x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G%$sinG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G%$cosG" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(f1(x)=f2(x),x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 85 "Nyn\355 si funkce nech\341me na p\370\355slu \232n\351m intervalu vykreslit, tedy na intervalu [0,Pi/2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "plot(\{sin(x),cos(x)\},x=0..Pi/2,co lor=black,style=line,font=[TIMES,ROMAN,11],scaling=constrained);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6*-%'CURVESG6#7S7$ $\"\"!F)F(7$$\"3NGK5j*))QU$!#>$\"3QsLeI+ABMF-7$$\"3DXXYUk*HS'F-$\"3]DS +L@i)R'F-7$$\"3=N68yVJ`(*F-$\"3_b&ehJeyt*F-7$$\"3%3h%eRSe78!#=$\"3<&Q% f]#=)38F=7$$\"3k+,hQPB[;F=$\"3V-yj65yS;F=7$$\"3'H#*ed(RUf>F=$\"3q)*)ys &)4p%>F=7$$\"3kHX[TMk\"G#F=$\"3G3RBS#)*=E#F=7$$\"3Saq%HF=$\"3=7dd?+e/HF=7$$\"3)pq'4OKt)G$F=$\"3c0jx $Rp(HKF=7$$\"3#f/N#RTo*e$F=$\"3ML>uye38NF=7$$\"3Ut79wN[GRF=$\"3V3zj5M@ GQF=7$$\"3/VrOc6q%F=7$$\"31\\,oR/A[_F=$\"3SMGBr+f5]F=7 $$\"3uvW/X(*RG,:eF=7$$\"3.n3p46^WlF=$\"33g0zi&Qs3'F=7$$\" 3oHyF.C6noF=$\"3h+)=j,t*RjF=7$$\"3(*zx.5Ir.sF=$\"3Qz3MFxj'f'F=7$$\"3'p z!QUu\"G^(F=$\"3$[8q$y.wDoF=7$$\"3A\"3@7LGi%yF=$\"3wm47uKelqF=7$$\"3)3 \"HIT&[D>)F=$\"3M(RvZssjI(F=7$$\"3gv)\\AI@S\\)F=$\"3C>#p\"po&)3vF=7$$ \"3vn()=V,i>))F=$\"3%4zeG%\\()>xF=7$$\"3'G:[dg&*f:*F=$\"31()\\)y]!GHzF =7$$\"3sSt6rL2&[*F=$\"3g&H%*=Uja7)F=7$$\"3mka(*HIZ.)*F=$\"3%3R7+w2pI)F =7$$\"3Em\"[l:+d,\"!#<$\"3Q?Zs+w\\)\\)F=7$$\"3c!3XyEmu/\"F_u$\"3Ih!)R3 tfh')F=7$$\"3sJ_*>P$Q\"3\"F_u$\"3VZPF_)*3E))F=7$$\"3.M\"G%4t676F_u$\"3 kW#3Hj\"Qm*)F=7$$\"3co*Q4iq'*z.@\"F_u$\"3Y(Q,up+vN*F=7$$\"34Q$[)>&*oU7F _u$\"3OZ!)zP7am%*F=7$$\"3I^lOFY^w7F_u$\"3-w%)pSt5q&*F=7$$\"3`!)f6EA448 F_u$\"3-KPDS[]f'*F=7$$\"3=;T7EvSU8F_u$\"3B\"='y#[C.u*F=7$$\"3a_wiepWv8 F_u$\"3$oY$>Q\"*z4)*F=7$$\"3U$obdw1eS\"F_u$\"3#4Wi\"*p+U')*F=7$$\"3s$) o#3`-1W\"F_u$\"3aZ!3__n`\"**F=7$$\"3-#*)4zFCK/mF=7$Fis$\"3Wp$f4=xjN'F=7$F^t$\"3#Gr \"zlF:$4'F=7$Fct$\"3+kbUhf'*GeF=7$Fht$\"3S\\$>&*yStc&F=7$F]u$\"3syV,H. Dq_F=7$Fcu$\"35cj1lEn(*\\F=7$Fhu$\"3DF8Py$y5q%F=7$F]v$\"3Cg[y,0kFWF=7$ Fbv$\"3Fz_\\X[#R7%F=7$Fgv$\"3R](>U([*Q$QF=7$F\\w$\"3G8u?D(Qm_$F=7$Faw$ \"38OldzS^AKF=7$Ffw$\"3gN^_O]_+HF=7$F[x$\"3]EKPO+F(e#F=7$F`x$\"3s9%3md %3kAF=7$Fex$\"3G+Nc*p#4T>F=7$Fjx$\"3v3+*zL?Ck\"F=7$F_y$\"3#R-7)3IE)H\" F=7$Fdy$\"3q![!=de+\"*)*F-7$Fiy$\"3?\")3+Q4@%e'F-7$F^z$\"370X.()zM7MF- 7$Fcz$\"3&pI?mi'*[9$!#E-%%FONTG6%%&TIMESG%&ROMANG\"#6-%&STYLEG6#%%LINE G-%'COLOURG6&%$RGBGF)F)F)-%+AXESLABELSG6$Q\"x6\"Q!F^el-%(SCALINGG6#%,C ONSTRAINEDG-%%VIEWG6$;F($\"+Fjzq:!\"*%(DEFAULTG" 1 6 0 1 10 0 2 6 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 140 " Na intervalu [0,Pi/4] plat\355 sin(x) \+ >= cos(x) a na intervalu [Pi/4,Pi/2] cos(x) >= sin(x). Budeme po\350 \355tat sou\350et dvou p\370\355slu\232n\375ch integr\341l\371." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "PL1:=Int(f2(x)-f1(x),x=0..P i/4)+Int(f1(x)-f2(x),x=Pi/4..Pi/2)=int(f2(x)-f1(x),x=0..Pi/4)+int(f1(x )-f2(x),x=Pi/4..Pi/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PL1G/,&-% $IntG6$,&-%$cosG6#%\"xG\"\"\"-%$sinGF-!\"\"/F.;\"\"!,$%#PiG#F/\"\"%F/- F(6$,&F0F/F+F2/F.;F6,$F7#F/\"\"#F/,&*$-%%sqrtG6#FAF/FAFAF2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }