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            復習指導(1)-2019年高等數學一復習資料-福建專升本

            福建成人高考信息網www.laiwobuy.com 發布時間: 2018年11月27日

            復習指導(1)

             (一)函數

              1、知識范圍

              (1)函數的概念

              函數的定義、函數的表示法、分段函數、隱函數

              (2)函數的性質

              單調性、奇偶性、有界性、周期性

              (3)反函數

              反函數的定義、反函數的圖像

              (4)基本初等函數

              冪函數、指數函數、對數函數、三角函數、反三角函數

              (5)函數的四則運算與復合運算

              (6)初等函數

              2、要求

              (1)理解函數的概念,會求函數的表達式、定義域及函數值,會求分段函數的定義域、函數值,會作出簡單的分段函數的圖像。

              (2)理解函數的單調性、奇偶性、有界性和周期性。

              (3)了解函數與其反函數之間的關系(定義域、值域、圖像),會求單調函數的反函數。

              (4)熟練掌握函數的四則運算與復合運算。

              (5)掌握基本初等函數的性質及其圖像。

              (6)了解初等函數的概念。

              (7)會建立簡單實際問題的函數關系式。

              (二)極限

              1、知識范圍

              (1)數列極限的概念

              數列、數列極限的定義

              (2)數列極限的性質

              唯一性、有界性、四則運算法則、夾通定理、單調有界數列極限存在定理

              (3)函數極限的概念

              函數在一點處極限的定義、左、右極限及其與極限的關系趨于無窮時函數的極限、函數極限的幾何意義

              (4)函數極限的性質

              唯一性、四則運算法則、夾通定理

              (5)無窮小量與無窮大量

              無窮小量與無窮大量的定義、無窮小量與無窮大量的關系、無窮小量的性質、無窮小量的階

              (6)兩個重要極限

              2、要求

              (1)理解極限的概念,會求函數在一點處的左極限與右極限,了解函數在一點處極限存在的充分必要條件。

              (2)了解極限的有關性質,掌握極限的四則運算法則。

              (3)理解無窮小量、無窮大量的概念,掌握無窮小量的性質、無窮小量與無窮大量的關系。會進行無窮小量階的比較(高階、低階、同階和等價)。會運用等價無窮小量代換求極限。

              (4)熟練掌握用兩個重要極限求極限的方法。


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