ΑΛΓΕΒΡΑ Β' ΛΥΚΕΙΟΥ - ΧΑΤΖΗΔΗΜΗΤΡΙΑΔΗΣ ΑΘΑΝΑΣΙΟΣ

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1.11. !\" x, y x + y = ,  ฀0  ฀0ȂǹĬǾȉǾȈǼʌȠȝȑȞȦȢĮȞıİȝȚĮİȟȓıȦıȘįȦ[2[[\ȒȠIJȚįȘʌȠIJİȐȜȜȠʌȜȘȞIJȘȢįȠșİȓıĮȢȝȠȡijȒȢIJȩIJİįİʌȡȩțİȚIJĮȚȖȚĮȖȡĮȝȝȚțȒİȟȓıȦıȘțĮȚįİʌĮȡȚıIJȐȞİȚİȣșİȓĮǻǹȈȀǹȁȅȈȆȠȜȪıȦıIJȐȂȚĮʌĮȡĮIJȒȡȘıȘȝȩȞȠİʌİȚįȒȠȚıȣȞIJİȜİıIJȑȢIJȦȞȝİIJĮȕȜȘIJȫȞİȓȞĮȚʌȡĮȖȝĮIJȚțȠȓĮȡȚșȝȠȓȖȚĮĮțĮȚȕȝʌȠȡȫȞĮʌȐȡȦȠʌȠȚȠȞįȒʌȠIJİĮȡȚșȝȩȡȘIJȩȒȐȡȡȘIJȠ2. # $ % \" \" 0 x+ y= . y=– x+ 0, y=– x+ =0, x= x= y y. =0, y= y= x x. & \" \" (x, y) .ȂǹĬǾȉǾȈǻȘȜĮįȒȠȚȜȪıİȚȢȝȚĮȢȖȡĮȝȝȚțȒȢİȟȓıȦıȘȢIJȘȢȝȠȡijȒȢĮ[ȕ\ ȖİȓȞĮȚȐʌİȚȡİȢǻǹȈȀǹȁȅȈǹțȡȚȕȫȢȅȚȜȪıİȚȢİȓȞĮȚȩȜĮIJĮıȘȝİȓĮ[\ IJȘȢİȣșİȓĮȢʌȠȣʌĮȡȚıIJȐȞİȚȘİȟȓıȦıȘȩIJĮȞȕȑȕĮȚĮIJĮĮțĮȚȕįİȞİȓȞĮȚIJĮȣIJȩȤȡȠȞĮ 2 x 2 xy xy5. & ! \" (x, y) .ȂǹĬǾȉǾȈDzȞĮıȪıIJȘȝĮȝʌȠȡİȓȞĮȑȤİȚʌĮȡĮʌȐȞȦĮʌȩȝȓĮȜȪıİȚȢǻǹȈȀǹȁȅȈĭȣıȚțȐĬȣȝȓıȠȣȩIJȚțȐșİȖȡĮȝȝȚțȒİȟȓıȦıȘʌĮȡȚıIJȐȞİȚİȣșİȓĮȉȓıȘȝĮȓȞİȚıȪıIJȘȝĮȀȠȚȞȑȢȜȪıİȚȢDzȤȦȜȠȚʌȩȞʌİȡȚʌIJȫıİȚȢȖȚĮIJȚȢȜȪıİȚȢİȞȩȢ[ȖȡĮȝȝȚțȠȪıȣıIJȒȝĮIJȠȢȂȠȞĮįȚțȒȜȪıȘIJİȝȞȩȝİȞİȢİȣșİȓİȢ ȀĮȝȓĮȜȪıȘĮįȪȞĮIJȠıȪıIJȘȝĮʌĮȡȐȜȜȘȜİȢİȣșİȓİȢ DZʌİȚȡİȢȜȪıİȚȢĮȩȡȚıIJȠıȪıIJȘȝĮȠȚįȪȠİȣșİȓİȢIJĮȣIJȓȗȠȞIJĮȚ 6. ! !.

7. # $ '! ! \" 2x2\" #! ! .$ #'.8. ( ) ! 2 x 2 (2 2 ): = !–9. ( ) ! \" ! ! ! \" xy xy ,D= , Dx = Dy =ȂǹĬǾȉǾȈȅȚȠȡȓȗȠȣıİȢIJȠȣıȣıIJȒȝĮIJȠȢİȓȞĮȚʌȡĮȖȝĮIJȚțȠȓĮȡȚșȝȠȓȆȫȢȝĮȢȕȠȘșȐȞİıIJȠȞĮȜȪıȠȣȝİȑȞĮıȪıIJȘȝĮǻǹȈȀǹȁȅȈȊʌȠȝȠȞȒǹȣIJȩșĮįİȓȟȦıIJȚȢʌĮȡĮțȐIJȦȖȡĮȝȝȑȢ10. & – !! xy % D 0, ! \" xy % D = 0, ! (x , y) = Dx , Dy DD .ȂǹĬǾȉǾȈȀĮIJȐȜĮȕĮǹʌȜȐȣʌȠȜȠȖȓȗȦIJȚȢȠȡȓȗȠȣıİȢIJȠȣıȣıIJȒȝĮIJȠȢțĮȚȟȑȡȦIJȚȢȜȪıİȚȢIJȠȣǻǹȈȀǹȁȅȈȈȦıIJȐȆĮȡĮțȐIJȦįȓȞȦțȐʌȠȚİȢȝİșȠįȠȜȠȖȓİȢțĮȚȤȡȒıȚȝĮıȤȩȜȚĮȖȚĮIJȘȞțȐșİʌİȡȓʌIJȦıȘȟİȤȦȡȚıIJȐǹȞįİțĮIJĮȜȐȕİȚȢțȐIJȚȝİȡȦIJȐȢȂǹĬǾȉǾȈǼȞIJȐȟİȚ



7. ! & f, , !& ,\" xA : –x A \" f (–x) = f (x)( ! )! . # Cf yy.8. *#!& ) f, , *#!& ),\" xA : –x A \" f (–x) = – f (x)( ! )! . # Cf \" .ȂǹĬǾȉǾȈ&IİȓȞĮȚȘțĮȝʌȪȜȘIJȘȢIȘȖȡĮȝȝȒIJȘȢIʌȐȞȦıIJȠȣȢȐȟȠȞİȢǻǹȈȀǹȁȅȈȃĮȚǵʌȦȢțĮIJĮȜĮȕĮȓȞİȚȢȠȚʌİȡȚııȩIJİȡİȢıȣȞĮȡIJȒıİȚȢįİȞİȓȞĮȚʌİȡȚIJIJȑȢȠȪIJİȐȡIJȚİȢȂȘȞĮʌȠȡȒıİȚȢĮȞįİȝʌȠȡȑıİȚȢȞĮțĮIJĮIJȐȟİȚȢȝȚĮȒʌİȡȚııȩIJİȡİȢıȣȞȐȡIJȘıİȚȢ+, – -1. ! &.) * ! .f, x \" f(x).2. ! &.) * ! ! \".3. ! &.) * ! . x$ f(x).f ,4. ! &.) * ! ! \"\" .5. ( ! )! , \". f



1.)i) f(x) = 3x – 1ii) g(x) = –3x – 1(! #& # $i) x1 , x2 x1 < x2 3 x1 < 3 x2Df = 3 x1 – 1 < 3 x2 – 1* f( x1 ) < f( x2 ) fii) x1 , x2 x1 < x2 –3 x1 > –3 x2Dg = –3 x1 – 1 > –3 x2 – 1 g( x1 ) > g( x2 ) g* «+ 4» +2. f(x) = 3x 1 1, + 3) 1, +(! #& # $ 3x 1 x 1, Df = 1, + 3, 3x – 1 0 x1 < x2 3 3* x1 , x2 1, + 1 x1 < x2 3 3 1 3 x1 < 3 x2 1 – 1 3 x1 – 1 < 3 x2 – 1 0 3 x1 – 1 < 3 x2 – 1 3x1 1 < 3x2 1 f( x1 ) < f( x2 ) -f



$%1. & & 2\" 1\" – 180 90 360 270 .ȂǹĬǾȉǾȈȂİIJĮʌȡȩıȘȝĮIJȓȖȓȞİIJĮȚǻǹȈȀǹȁȅȈĬİȦȡȫ ȑȞĮ ȖȦȞȓĮ ıIJȠȠIJİIJĮȡIJȘȝȩȡȚȠțĮȚȕȡȓıțȦıİʌȠȚȠIJİIJĮȡIJȘȝȩȡȚȠİȓȞĮȚȘȗȘIJȠȪȝİȞȘȖȦȞȓĮȆȡȑʌİȚȜȠȚʌȩȞȞĮȖȞȦȡȓȗȦIJĮʌȡȩıȘȝĮȩȜȦȞIJȦȞIJȡȚȖȦȞȠȝİIJȡȚțȫȞĮȡȚșȝȫȞıİțȐșİIJİIJĮȡIJȘȝȩȡȚȠȖȚĮȞĮȕȡȦIJȠİțȐıIJȠIJİʌȡȩıȘȝȠ. # (180 + ) = ; ,. 180 + ( 180 + ), ,.! (180 + ) = –. !(270 – ) = ; , 270 – , ( 270 – ), , ! (270 – ) =ǻǹȈȀǹȁȅȈǼȞȞȠİȓIJĮȚʌȦȢIJȠʌĮȡĮʌȐȞȦıțİʌIJȚțȩįİȞIJȠʌĮȡȠȣıȚȐȗȠȣ—İıIJȚȢĮıțȒıİȚȢ2. (–) #\" & ' &&(–) , « ȝʌĮȓȞİȚȝȑıĮ » țĮȚıȤȘȝĮIJȓȗİȚ , «ȝʌĮȓȞİȚȝȑıĮ» ȝȩȞȠıȤȘȝĮIJȓȗȠȞIJĮȢIJȩȟĮȒIJȩȟĮʌȠȣįȚĮijȑȡȠȣȞțĮIJĮȝȠȓȡİȢıȣȞȦ ıȣȞȦ – = (– ) , – = (– ) , – = (– )– = (180 – )



ȝ ! \"# $ \"ȂǹĬǾȉǾȈǹȣIJȠȓİȓȞĮȚȠȚʌİȡȚȠȡȚıȝȠȓȖȚĮIJȠȣȢʌĮȡȠȞȠȝĮıIJȑȢȆİȚȡȐȗİȚȞĮIJȠȣȢʌȐȡȦȟİȤȦȡȚıIJȐȖȚĮIJȠȞțȐșİʌĮȡȠȞȠȝĮıIJȒʌȡȚȞȕȡȦIJȠǼȀȆǻǹȈȀǹȁȅȈǵȤȚȕȑȕĮȚĮ% ȝ ! & $\" '(')' ! \"# #*' $ % & ' (' % 'ȂǹĬǾȉǾȈȆȫȢșĮțȐȞȦĮʌĮȜȠȚijȒĮȞįİȞȟȑȡȦIJȠʌȡȩıȘȝȠIJȠȣǼȀȆǻǹȈȀǹȁȅȈǻȚĮțȡȓȞȦʌİȡȚʌIJȫıİȚȢțĮȚȜȪȞȦįȪȠijȠȡȑȢIJȘȞĮȞȓıȦıȘțȐIJȦĮʌȩįȚĮijȠȡİIJȚțȠȪȢʌİȡȚȠȡȚıȝȠȪȢȀĮȜȪIJİȡĮȞĮĮʌȠijİȪȖİIJĮȚǹțȠȜȠȣșȫȜȠȚʌȩȞIJȘȞİȟȒȢįȚĮįȚțĮıȓĮǼȀȆʌİȡȚȠȡȚıȝȠȓǵȜĮıIJȠĮǯȝİȜȠȢȅȝȩȞȣȝĮțĮȚʌȡȐȟİȚȢȂİIJĮIJȡȑʌȦIJȠʌȘȜȓțȠıİȖȚȞȩȝİȞȠǺȡȓıțȦIJȚȢȜȪıİȚȢIJȘȢĮȞȓıȦıȘȢȖȚĮIJȠȖȚȞȩȝİȞȠİȟĮȚȡȫȞIJĮȢIJȚȢIJȚȝȑȢʌȠȣȝȘįİȞȓȗȠȣȞIJȠȣȢĮȡȤȚțȠȪȢʌĮȡȠȞȠȝĮıIJȑȢʌİȡȚȠȡȚıȝȠȓ  ,--. \") *' ' & / 0 ,--. . + ,- & -& ./0 & !( !( ıȣȞȒșȦȢıIJȠIJİIJȡȐȖȦȞȠ - ǹȞIJȠȑȞĮȝȑȜȠȢȝʌȠȡİȓȞĮʌȐȡİȚțĮȚșİIJȚțȑȢțĮȚĮȡȞȘIJȚțȑȢIJȚȝȑȢȤȦȡȓȗȦʌİȡȚʌIJȫıİȚȢ1 & 2 -34\" \"# $ \" + -* -* . \" 12 3 415 3 %16 7 41 3 8$ ( !( 16ȂǹĬǾȉǾȈȅȚĮȞIJȓıIJȡȠijİȢȑȤȠȣȞʌȐȞIJĮıȣȝȝİIJȡȚțȠȪȢıȣȞIJİȜİıIJȑȢĮʌȩIJĮȐțȡĮʌȡȠȢIJĮȝȑıĮǻǹȈȀǹȁȅȈȃĮȚǼȓȞĮȚʌȠȜȪİȚįȚțȒʌİȡȓʌIJȦıȘǹijȠȪįȚĮȚȡȑıȦțȐșİȩȡȠȝİ16 ș& 1 8=  Ȓ1 1 \ĮȞȐȜȠȖĮȝİIJȘȞʌİȡȓʌIJȦıȘ 1



ϭϲϵ5.2 : x= log ฀ ฀= x : >0 ฀1, > 0log ฀ ,2. ʌȠȣʌȡȠțȪʌIJȠȣȞ log x = x log = log 1= 0 log = 13.log ( 1 2 ) = log 1 + log 2log 1 = log 1 – log 2 2log = log ,log = log 1 1 log , 2 =4.\" #$ != ! != : log10 = log 10 e loge = ln5. 10x= ln = x ex =log = x6. %& ' (! log >0 0< , 1log , log