Calculus 1 T Ch

  • November 2019
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‫ﺑﺴﻤﮫ ﺗﻌﺎﻟﯽ‬

‫ﺳﻮاﻻ ت اﻣﺘﺤﺎﻧﯽ ‪ :‬رﯾﺎﺿﯽ ﻋﻤﻮﻣﯽ ‪١‬‬

‫ﺳﺎﻋﺖ ﺷﺮوع‪١٢ :‬‬

‫رﺷﺘﮫ‪ :‬ﺷﯿﻤﯽ‬

‫ﻣﺪت اﻣﺘﺤﺎن ‪:‬‬

‫ﻧﺎم و ﻧﺎم ﺧﺎﻧﻮادﮔﯽ ‪:‬‬ ‫ﺳﺎل ﺗﺤﺼﯿﻠﯽ‪:‬‬

‫ﻧﯿﻢ ﺳﺎل ‪ :‬دوم‬

‫‪١٢٠‬‬

‫دﻗﯿﻘﮫ‬

‫ﺗﺎرﯾﺦ اﻣﺘﺤﺎن‪١٣٨۵/ ۴ / ٢١ :‬‬

‫‪٨۴- ٨۵‬‬

‫داﻧﺸﮕﺎه آزاد اﺳﻼﻣﯽ ﺗﺒﺮﯾﺰ‬

‫ﺑﺎرم‬

‫‪z 4 − 2z 2 + 4 = 0‬‬

‫‪ .١‬ﻣﻌﺎدﻟﮫ زﯾﺮ را ﺣﻞ ﮐﻨﯿﺪ‪.‬‬

‫‪٢‬‬

‫‪ .٢‬ﺣﺪود زﯾﺮ را در ﺻﻮرت وﺟﻮد ﺑﮫ دﺳﺖ آورﯾﺪ‪.‬‬

‫اﻟﻒ( ‪lim+ (1 + sin 4x )cot gx‬‬

‫ب(‬

‫‪x →0‬‬

‫‪1 + tgx − 1 + sin x‬‬ ‫‪x3‬‬

‫‪lim‬‬

‫‪x →0‬‬

‫‪۴‬‬

‫‪n‬‬

‫‪1 2‬‬ ‫‪k ‬‬ ‫ج( )) ‪lim+ ( x (   +   + K +  ‬‬ ‫‪x →0‬‬ ‫‪x  x ‬‬ ‫‪x ‬‬

‫د(‬

‫‪n‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫∞→ ‪n‬‬ ‫‪k =1 n + k‬‬ ‫∑ ‪lim‬‬

‫‪ .٣‬ﺑﺮای ﭼﮫ ﻣﻘﺎدﯾﺮی از ‪ x‬ﺗﺎﺑﻊ زﯾﺮ ﭘﯿﻮﺳﺘﮫ اﺳﺖ‪.‬‬

‫‪x ∈¤‬‬

‫‪x ∉¤‬‬ ‫‪ .۴‬ﻣﺸﺘﻖ ﭘﺬﯾﺮی ﺗﺎﺑﻊ زﯾﺮ را در ﻧﻘﻄﮫ ‪ x = 0‬ﺑﺮرﺳﯽ ﮐﻨﯿﺪ‪.‬‬

‫‪x =0‬‬

‫‪0‬‬ ‫‪‬‬ ‫‪f (x ) =  2‬‬ ‫‪1‬‬ ‫‪x‬‬ ‫‪sin‬‬ ‫‪‬‬ ‫‪x‬‬

‫‪x ≠0‬‬ ‫‪ .۵‬ﻣﺸﺘﻖ ﺗﻮاﺑﻊ زﯾﺮ را ﺑﺪﺳﺖ آورﯾﺪ‪.‬‬ ‫(‬

‫اﻟﻒ(‬

‫‪x‬‬ ‫‪tg ( ) = x + y‬‬ ‫‪y‬‬

‫ب(‬

‫‪x‬‬ ‫‪f (x ) = ‬‬ ‫‪0‬‬

‫‪١٫۵‬‬

‫‪١٫۵‬‬

‫‪y = (sin x ) x‬‬ ‫‪۴‬‬ ‫‪x3‬‬

‫ج( )) ‪y = ln(ln 2 (ln 3 x‬‬

‫د(‬

‫‪t cos(t )dt‬‬

‫∫‬

‫= ) ‪g (x‬‬

‫‪x‬‬

‫ﻧﺎم و ﻧﺎم ﺧﺎﻧﻮادﮔﯽ اﺳﺘﺎد‪ :‬اﺳﻤﺎﻋﯿﻞ ﻋﻠﯿﺰاده‬

‫اﻣﻀﺎء‬

‫ﺟﻤﻊ ﻧﻤﺮه‬

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