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# 345 by smoufer01

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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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