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                                                                ‫1-*ﺗﺤﺪﻳﺪ اﻟﻌﺪد اﻟﻤﺸﺘﻖ ﻋﻠﻰ اﻟﻴﻤﻴﻦ ﻓﻲ 1‬
                                                                                                 ‫ﻟﺪﻳﻨﺎ:‬
                                                                                                ‫1‬
                                                                                        ‫1+ − 1− ‪x‬‬
                                                                 ‫)1( ‪g ( x) − g‬‬                 ‫‪x‬‬
                                                          ‫‪lim‬‬                   ‫‪= lim‬‬
                                                           ‫1→ ‪x‬‬
                                                           ‫1 ‪x‬‬
                                                                     ‫1− ‪x‬‬          ‫1→ ‪x‬‬
                                                                                   ‫1 ‪x‬‬
                                                                                           ‫1− ‪x‬‬

                                                                                                      ‫1− ‪x‬‬
                                                                                              ‫+1− ‪x‬‬
                                                                                  ‫‪= lim‬‬                 ‫‪x‬‬
                                                                                     ‫1→ ‪x‬‬
                                                                                     ‫1 ‪x‬‬
                                                                                                   ‫1− ‪x‬‬
                                                                                                      ‫1‬
                                                                                         ‫+ 1 ‪= lim‬‬      ‫2=‬
                                                                                            ‫1→ ‪x‬‬      ‫‪x‬‬
                                                                                            ‫1 ‪x‬‬


                                                                                      ‫إذن 2 = )1( ‪g ' d‬‬
                                                              ‫*ﺗﺤﺪﻳﺪ اﻟﻌﺪد اﻟﻤﺸﺘﻖ ﻋﻠﻰ اﻟﻴﺴﺎر ﻓﻲ 1‬
                                                                                              ‫ﻟﺪﻳﻨﺎ :‬

                                                                                                ‫1‬
                                                                                     ‫− 1− ‪x‬‬       ‫1+‬
                                                            ‫)1( ‪g ( x) − g‬‬                      ‫‪x‬‬
                                                      ‫‪lim‬‬                  ‫‪= lim‬‬
                                                       ‫1→ ‪x‬‬
                                                       ‫1≺ ‪x‬‬
                                                                ‫1− ‪x‬‬          ‫1→ ‪x‬‬
                                                                              ‫1≺ ‪x‬‬
                                                                                             ‫1− ‪x‬‬
                                                                                                   ‫1− ‪x‬‬
                                                                                  ‫+ )1 − ‪−( x‬‬
                                                                        ‫‪= lim‬‬                        ‫‪x‬‬
                                                                           ‫1→ ‪x‬‬
                                                                           ‫1≺ ‪x‬‬
                                                                                          ‫1− ‪x‬‬
                                                                                                   ‫1‬
                                                                              ‫+ 1 − ‪= lim‬‬            ‫0=‬
                                                                                  ‫1→ ‪x‬‬             ‫‪x‬‬
                                                                                  ‫1≺ ‪x‬‬

                                                                                 ‫إذن: 0 = )1( ‪g ' g‬‬
                                                                        ‫2- ﺗﺤﺪﻳﺪ اﻟﻤﻘﺎرب اﻟﻤﺎﺋﻞ:‬
                                                                                           ‫1‬
                                          ‫ﻟﻜﻞ ‪ x‬ﻣﻦ [∞+ ,1]‬             ‫ﻟﺪﻳﻨﺎ: − 1 − ‪g ( x) = x‬‬
                                                                                            ‫‪x‬‬
                                                                                      ‫1−‬
                                                   ‫‪lim g ( x) − ( x − 1) = lim‬‬            ‫إذن: 0 =‬
                                                   ‫∞+→ ‪x‬‬                    ‫∞−→ ‪x‬‬      ‫‪x‬‬

                  ‫وهﺬا ﻳﻌﻨﻲ أن اﻟﻤﺴﺘﻘﻴﻢ ذا اﻟﻤﻌﺎدﻟﺔ 1-‪ y = x‬هﻮ ﻣﻘﺎرب ﻣﺎﺋﻞ ﻟﻠﻤﻨﺤﻨﻰ ) ‪ (Cg‬ﺑﺠﻮار ∞+‬

								
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