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10vD0&z4G&F`p7$$\"1#**\\il!=:*)F`p$\"1E\"yJhE8H&F`p7$$\"1$****\\U%>&F`p7$$\"1%***** \\#y'G**F`p$\"1R76RivM]F`p7$$\"1***\\iZ!)y.\"F1$\"1+VnMip(y%F`p7$$\"1* ***\\FJ*G3\"F1$\"1quI=Gb)[%F`p7$$\"1***\\(yd!z7\"F1$\"1\"y4HD2*eTF`p7$ $\"1******H%=H<\"F1$\"1XfzP(ou\"QF`p7$$\"1mm;*HkL@\"F1$\"1Gh^_cw7NF`p7 $$\"1LLLo,\"QD\"F1$\"1J(Q!Ry4=KF`p7$$\"1****\\PgD%H\"F1$\"1c%[%4%R'QHF `p7$$\"1mmm1>qM8F1$\"1`gOYI\\xEF`p7$$\"1LLL.62@9F1$\"1)[p?Y(e'=#F`p7$$ \"1++++.W2:F1$\"1@KRHb^%y\"F`p7$$\"1mm;HOq&e\"F1$\"1rslKSJ5F`p7$$\"1+ ++S>4N=F1$\"1L9y`W'Hf)FH7$$\"1mmm6s5'*>F1$\"1,y6>(p3?'FH7$$\"1+++lXTk@ F1$\"113Ze!zE^%FH7$$\"1mmmmd'*GBF1$\"1`b[6^!yP$FH7$$\"1+++DcB,DF1$\"1Y B(3\\`Xa#FH7$$\"1MLLt>:nEF1$\"11E2')fiq>FH7$$\"1LLL.a#o$GF1$\"1Z4CgA7T :FH7$$\"1nmm^Q40IF1$\"1bx'*pcbC7FH7$$\"1+++!3:(fJF1$\"1bjp&)3C-5FH7$$ \"1nmmc%GpL$F1$\"15qJf?Jf!)F-7$$\"1LLL8-V&\\$F1$\"1=+')3h8&p'F-7$$\"1+ ++XhUkOF1$\"1lB63CmVbF-7$$\"1+++:o " 0 "" {MPLTEXT 1 0 30 "I nt(f(x), x=0..d): %=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$I ntG6$*&*$)%\"xG\"\"#\"\"\"F,,&*$)F*\"\"'F,\"\"\"F1F1!\"\"/F*;\"\"!%\"d G,$-%'arctanG6#*$)F6\"\"$F,#F1F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Limit(rhs(%), d=infinity): %=value(%);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/-%&LimitG6$,$-%'arctanG6#*$)%\"dG\"\"$\"\"\"#\" \"\"F./F-%)infinityG,$%#PiG#F1\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Int(f(x), x=-infinity..infinity): %=value(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&*$)%\"xG\"\"#\"\"\"F,,&*$) F*\"\"'F,\"\"\"F1F1!\"\"/F*;,$%)infinityG!\"\"F6,$%#PiG#F1\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=x->1/(sqrt(x)*(x+1));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowG F(*&\"\"\"F-*&-%%sqrtG6#9$\"\"\",&F2\"\"\"F5F5\"\"\"!\"\"F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(f(x), x=0..4, y=0..4); " }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7fn7$$\"1+++m;')=()!#<$\" 1h$o\"[80:J!#:7$$\"1*****z-Trm*F*$\"1Rvy**fuKHF-7$$\"1+++R?ah5!#;$\"1$ yNs.)puFF-7$$\"1+++w*pj:\"F6$\"1\"\\c=`)*ej#F-7$$\"1+++7z>^7F6$\"13)e, 1'o7DF-7$$\"1+++&y`3W\"F6$\"1k:W,&pEI#F-7$$\"1+++e'40j\"F6$\"1Q^(eH8$H @F-7$$\"1+++BvzV=F6$\"19<%3#>Jm>F-7$$\"1+++)Q&3d?F6$\"1$esh%QlG=F-7$$ \"1+++`KPqAF6$\"1_9T#)QQ5(>%F6$\"1v+Az:A(3\"F-7$$\"1+++\">K'*)\\ F6$\"16Gfi$3WW*F67$$\"1+++Dt:5eF6$\"1uE0C=$zH)F67$$\"1+++\"fX(emF6$\"1 *pb6\"\\LctF67$$\"1+++DCh/vF6$\"1d%ydoAXf'F67$$\"1+++L/pu$)F6$\"1+M[4y 'p%fF67$$\"1+++;c0T\"*F6$\"1m([$pwJkaF67$$\"1+++I,Q+5F-$\"15k(>)**4)* \\F67$$\"1+++]*3q3\"F-$\"1=)4u\"*ydf%F67$$\"1+++q=\\q6F-$\"1?Wy]'4&eUF 67$$\"1+++fBIY7F-$\"1))p*G'zn()RF67$$\"1+++j$[kL\"F-$\"1y%QD(oE-PF67$$ \"1+++`Q\"GT\"F-$\"1*QnKd`o[$F67$$\"1+++s]k,:F-$\"1QJ%[M]?E$F67$$\"1++ +`dF!e\"F-$\"1'yU&3o&H3$F67$$\"1+++sgam;F-$\"1YCvvR(\\!HF67$$\"1+++F- $\"1V#)p![;=[#F67$$\"1+++Uc-)*>F-$\"1+%f!e)R(fBF67$$\"1+++f`@'3#F-$\"1 T$4NONLC#F67$$\"1+++nZ)H;#F-$\"1K9L[;p\\@F67$$\"1+++Ky*eC#F-$\"1f]TC$ \\d0#F67$$\"1+++S^bJBF-$\"1#G+-Wed'>F67$$\"1+++0TN:CF-$\"1: $GF-$\"1r2rB:r]:F67$$\"1+++qfa " 0 "" {MPLTEXT 1 0 43 "Int(f(x), x=0..1)+Int(f(x), x=1..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,&-%$IntG6$*&\"\"\"F(*&-%%sqrtG6#%\"xGF(,&F-\"\"\"F/F/\"\"\"!\"\"/F-; \"\"!F/F/-F%6$F'/F-;F/%)infinityGF/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(c>0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Int(f(x), x=c..1): %=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/-%$IntG6$*&\"\"\"F(*&-%%sqrtG6#%\"xGF(,&F-\"\"\"F/F/\"\"\"!\"\"/F-; %#c|irGF/,&%#PiG#F/\"\"#-%'arctanG6#*$-F+6#F4F(!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Limit(rhs(%), c=0, right): %=value(%);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&LimitG6%,&%#PiG#\"\"\"\"\"#-%'arc tanG6#*$-%%sqrtG6#%#c|irG\"\"\"!\"#/F3\"\"!%&rightG,$F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Int(f(x), x=1..c): %=value(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(*&-%%sqrtG6#%\"xGF (,&F-\"\"\"F/F/\"\"\"!\"\"/F-;F/%#c|irG,&-%'arctanG6#*$-F+6#F4F(\"\"#% #PiG#!\"\"F<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "Limit(rhs(% ), c=+infinity): %=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&Li mitG6$,&-%'arctanG6#*$-%%sqrtG6#%#c|irG\"\"\"\"\"#%#PiG#!\"\"F1/F/%)in finityG,$F2#\"\"\"F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Protoze o ba dilci integraly konverguji, konverguje i nas integral a plati" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Int(f(x), x=0..infinity)=Pi/ 2+Pi/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(*&-%%sq rtG6#%\"xGF(,&F-\"\"\"F/F/\"\"\"!\"\"/F-;\"\"!%)infinityG%#PiG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "2" 0 } {VIEWOPTS 1 1 0 1 1 1803 }