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					           ‫ا‬
   ‫1‬
       ‫2‬
                                                                                                      ‫ت‬               ‫آ ا‬        ‫ا‬
  ‫22‪C :NS‬‬                                      ‫آ ر‬              ‫ا‬         ‫نا‬    ‫ا‬
                                                     ‫7002(‬          ‫) ا ورة ا د‬
       ‫3‬           ‫ز:‬       ‫ةا‬                                       ‫ع‬        ‫ا‬                                  ‫ت‬          ‫ا دة: ا‬

       ‫7‬       ‫:‬        ‫ا‬
                                                           ‫م ا را‬        ‫+ا‬         ‫ما‬       ‫+ا‬        ‫ا‬         ‫ما‬    ‫)ة( : ا‬             ‫ا‬



                        ‫(‬        ‫ا‬                     ‫ا‬            ‫لا‬                   ‫)‬


                                                                                                    ‫ا ول : ) 3 ن(‬            ‫ا‬

            ‫د ه :‬         ‫)‪ (S‬ا‬ ‫) ‪ ( o, i , j , k‬ا‬                 ‫بإ‬       ‫ءا‬   ‫ا‬
                                                        ‫2‬   ‫2‬   ‫2‬
‫ى )‪ (P‬ا ي د ه : 0 = 1 + ‪. x – y + 2z‬‬               ‫0 = 8 + ‪ x + y + z - 2x - 4y - 6z‬و ا‬
                                                                                                                                     ‫1‬
                      ‫وي 6 .‬           ‫)3,2 ,1( ‪ Ω‬أن‬       ‫)‪ (S‬ه ا‬     ‫ان آ ا‬       ‫1(‬
                                            ‫)‪. (S‬‬       ‫ى )‪ (P‬س‬        ‫أن ا‬         ‫2(‬                                               ‫57,0‬
                    ‫)‪. (P‬‬    ‫)∆( ا ر ‪ Ω‬و ا دي‬                       ‫را‬         ‫3( أ- د‬                                               ‫5,0‬
                                                                                                                                     ‫57,0‬
                                    ‫س )‪ (P‬و)‪. (S‬‬            ‫ثإ ا ت‪ω‬‬          ‫ب- د‬

                                                                                                  ‫: ) 3 ن(‬        ‫ا‬          ‫ا‬


                                             ‫ا ي ا د ا ي 2) ‪(3 – 2i‬‬          ‫ا‬    ‫5,0 1( أ- أآ‬
             ‫2‬
           ‫‪ ℂ‬ا د : 0 = ‪z – 2(4 + i )z + 10 + 20i‬‬          ‫ا اد ا‬               ‫ب-‬           ‫1‬
  ‫أ‬         ‫‪ A‬و ‪ B‬و‪ C‬ا‬    ‫) ‪ ( O, u , v‬ا‬                     ‫بإ‬     ‫ىا يا‬       ‫ا‬        ‫2(‬
                                           ‫ا ا ه : ‪ a = 1 + 3i‬و‪ b = 7 – i‬و ‪. c = 5 + 9i‬‬
                                                                                              ‫‪c−a‬‬
                                                                                                  ‫أن : ‪= i‬‬       ‫أ-‬                  ‫5,0‬
                                                                                              ‫‪b−a‬‬
                                         ‫ا او .‬             ‫و‬             ‫وي ا‬      ‫‪ABC‬‬             ‫أن ا‬       ‫ب- ا‬                  ‫1‬

                                                                                                   ‫: ) 5,2 (‬      ‫ا‬          ‫ا‬

                                                                               ‫2‪x‬‬                ‫1‬
                                             ‫}1−{ − ‪. ℝ‬‬              ‫‪x‬‬             ‫+ 1− ‪= x‬‬         ‫ان :‬              ‫1(‬             ‫5,0‬
                                                                              ‫1+ ‪x‬‬             ‫1+ ‪x‬‬
                                                                                             ‫2‬
                                                                                         ‫‪2 x‬‬
                                                                                     ‫0∫ .‬       ‫أن : 3 ‪dx = ln‬‬        ‫2(‬             ‫1‬
                                                                                          ‫1+ ‪x‬‬
                                         ‫2‬                   ‫3‬
                                     ‫∫‬       ‫أن : 3 ‪x ln( x + 1)dx = ln‬‬              ‫اء ،‬                  ‫ل‬          ‫3(‬
                                     ‫0‬                       ‫2‬                                                                       ‫1‬


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                           ‫ا‬
                  ‫2‬
                                        ‫آ ر‬                    ‫ا‬    ‫نا‬      ‫ا‬                                             ‫ت‬                   ‫ا‬                             ‫ا دة :‬
                          ‫2‬                                 ‫) ا ورة ا د 7002(‬
                                                                 ‫ع‬      ‫ا‬     ‫م‬                             ‫+ا‬             ‫ا‬                      ‫ما‬           ‫ا‬        ‫)ة(‬            ‫ا‬
 ‫22‪C :NS‬‬                                                                                                             ‫م ا را‬         ‫+ا‬                         ‫ا‬

                                                                                                                                   ‫ا ا :) 5,2 (‬                                    ‫ا‬

                                       ‫اد 0 و0 و0 و1- و 1 و1 و 1‬                                         ‫ا‬            ‫ت‬                                                ‫يآ‬
                                                              ‫(.‬                                          ‫ت‬                ‫ا‬                           ‫ا‬                  ‫)‬
                                     ‫.‬   ‫ت ا‬        ‫ث‬      ‫ن وا‬                                         ‫ا و‬                              ‫:‬             ‫ا‬                ‫ا‬

                                                                                                                                     ‫:‬                 ‫اث ا‬                 ‫ا‬
                                     ‫".‬                     ‫ا‬              ‫تا‬           ‫ا‬                 ‫ا د0‬                                     ‫أ‬                        ‫‪":A‬‬
                                                                 ‫".‬                                     ‫أ ادا‬              ‫ت‬                  ‫ث‬                             ‫‪":B‬‬
                                              ‫م".‬                           ‫ا‬           ‫تا‬                 ‫ا‬                       ‫اد ا‬            ‫عا‬                       ‫‪":C‬‬

                                          ‫2‬                                                                                                                                                 ‫5,2‬
                                                ‫ث‪C‬ه‬                    ‫لا‬           ‫أن ا‬                     ‫‪ A‬و‪C‬‬                   ‫ا‬                  ‫لآ‬               ‫ا‬              ‫ا‬
                                          ‫7‬

                                                                                                                         ‫: ) 9 ن(‬
                      ‫: 1 − ‪. g ( x) = e + x‬‬       ‫‪ℝ‬‬‫‪−x‬‬
                                                                                                             ‫ا ا ا د ‪g‬ا‬           ‫‪(I‬‬
   ‫]0 ,∞−] .‬              ‫[∞+ ,0 [ و‬         ‫أن ‪ g‬ا‬                                                      ‫‪ ℝ‬ا‬    ‫‪x‬‬    ‫)‪g ‘(x‬‬       ‫1( ا‬                                                     ‫57,0‬
‫‪.ℝ‬‬     ‫‪x‬‬     ‫أن 1 ≥ ‪e− x + x‬‬       ‫أن 0 = )0(‪ ( g‬ا‬                                                       ‫‪)ℝ‬‬   ‫‪x‬‬   ‫أن 0 ≥ )‪g ( x‬‬     ‫2(‬                                                      ‫5,0‬
                                        ‫‪x‬‬
                          ‫= )‪f ( x‬‬                   ‫:‬                                  ‫‪x‬ا‬                   ‫ا‬             ‫‪f‬‬            ‫ا ا ا د‬                               ‫‪(II‬‬
                                     ‫‪x + e− x‬‬
                                          ‫) ‪. ( o, i , j‬‬                                                     ‫ا ‪f‬‬     ‫ا‬                                 ‫)‪ (C‬ا‬                   ‫و‬
                                   ‫ال ‪. ( (2(I‬‬                    ‫ا‬             ‫ل‬           ‫ا‬               ‫ا ا ‪ f‬ه ‪)ℝ‬‬                                      ‫أن‬                  ‫1(‬          ‫5,0‬
                                                                                                                                          ‫1‬
                                                                                        ‫*‪ℝ‬‬              ‫‪x‬‬             ‫= )‪f ( x‬‬                             ‫أن :‬             ‫2( أ –‬         ‫52,0‬
                                                                                                                 ‫1‬
                                                                                                           ‫‪1+ x‬‬
                                                                                                                ‫‪xe‬‬
                               ‫.‬          ‫ا‬             ‫ه‬             ‫أول ه‬         ‫أن : 0 = )‪ lim f ( x‬و 1 = )‪lim f ( x‬‬
                                                                                    ‫∞+→ ‪x‬‬                              ‫∞−→ ‪x‬‬
                                                                                                                                                                         ‫ب–‬                 ‫5,1‬
                                                                                                                                         ‫‪−x‬‬
                                                                                                                        ‫‪(1 + x)e‬‬
                                                                           ‫‪.ℝ‬‬           ‫‪x‬‬               ‫== )‪f '( x‬‬                                ‫أن :‬                 ‫3(أ–‬                ‫57,0‬
                                                                                                                        ‫) ‪(x + e‬‬    ‫2 ‪−x‬‬


                                                                   ‫ات ا ا ‪. f‬‬  ‫ول‬                                       ‫ب- ادرس إ رة )‪f ‘(x‬‬                                                 ‫5,0‬
                                                ‫.‬                ‫ا‬     ‫‪O‬أ‬     ‫)‪ (C‬ا‬                                       ‫د ا س‬        ‫4( أ- اآ‬                                             ‫5,0‬
                                                                                                              ‫)‪xg ( x‬‬
     ‫‪.ℝ‬‬           ‫ادرس إ رة )‪x − f ( x‬‬                                ‫‪ℝ‬‬         ‫‪x‬‬               ‫= )‪x − f ( x‬‬            ‫أن :‬                                             ‫ب-‬                ‫57,0‬
                                                                                                             ‫1 + )‪g ( x‬‬
                      ‫ه :‪.y=x‬‬                       ‫د‬           ‫)∆( ا ي‬                     ‫)‪ (C‬و ا‬                                  ‫ا‬                     ‫ا‬            ‫ج- ا‬               ‫52,0‬
                                                                  ‫1‬
                                                            ‫(.‬        ‫6 ,0− ≃‬                       ‫) ‪) ( o, i , j‬‬             ‫ا‬         ‫)∆( و)‪(C‬‬                           ‫5( أ‬             ‫1‬
                                                                 ‫‪1− e‬‬
         ‫‪.ℕ‬‬           ‫‪n‬‬            ‫1 = 0‪ U‬و ) ‪Un+1 = f ( Un‬‬                                                          ‫ا د )‪ (Un‬ا‬                                    ‫ا‬           ‫‪(III‬‬
                                                                                            ‫‪ℕ‬‬            ‫‪n‬‬            ‫أن 1 ≤ ‪0 ≤ U n‬‬                                            ‫1(‬          ‫5,0‬
                                      ‫ال ‪(4(II‬ب(.‬                      ‫ا‬            ‫ل‬               ‫ا‬            ‫)‬         ‫)‪(Un‬‬   ‫أن ا‬                                          ‫2(‬          ‫5,0‬
                                                                                                ‫.‬            ‫د‬            ‫أن )‪ (Un‬ر‬                                           ‫3( ا‬         ‫57,0‬


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