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            2016年成人高考專升本數學復習資料-復習指導二

            福建成人高考信息網www.laiwobuy.com 發布時間: 2015年11月04日

            二、一元函數微分學

            (一)導數與微分

            1.知識范圍

              (1)導數概念

              導數的定義 左導數與右導數 函數在一點處可導的充分必要條件 導數的幾何意義與物理意義 可導與連續的關系

              (2)求導法則與導數的基本公式

              導數的四則運算 反函數的導數 導數的基本公式

              (3)求導方法

              復合函數的求導法 隱函數的求導法 對數求導法 由參數方程確定的函數的求導法 求分段函數的導數

              (4)高階導數

              高階導數的定義 高階導數的計算

              (5)微分

              微分的定義 微分與導數的關系 微分法則 一階微分形式不變性

            2.要求

              (1)理解導數的概念及其幾何意義,了解可導性與連續性的關系,掌握用定義求函數在一點處的導數的方法。

              (2)會求曲線上一點處的切線方程與法線方程。

              (3)熟練掌握導數的基本公式、四則運算法則及復合函數的求導方法,會求反函數的導數。

              (4)掌握隱函數求導法、對數求導法以及由參數方程所確定的函數的求導方法,會求分段函數的導數。

              (5)理解高階導數的概念,會求簡單函數的 階導數。

              (6)理解函數的微分概念,掌握微分法則,了解可微與可導的關系,會求函數的一階微分。

            (二)微分中值定理及導數的應用

            1.知識范圍

              (1)微分中值定理

              羅爾(Rolle)定理 拉格朗日(Lagrange)中值定理

              (2)洛必達(L‘Hospital)法則

              (3)函數增減性的判定法

              (4)函數的極值與極值點 最大值與最小值

              (5)曲線的凹凸性、拐點

              (6)曲線的水平漸近線與鉛直漸近線

            2.要求

              (1)理解羅爾定理、拉格朗日中值定理及它們的幾何意義。會用羅爾定理證明方程根的存在性。會用拉格朗日中值定理證明簡單的不等式。

              (2)熟練掌握用洛必達法則求各種型未定式的極限的方法。

              (3)掌握利用導數判定函數的單調性及求函數的單調增、減區間的方法,會利用函數的單調性證明簡單的不等式。

              (4)理解函數極值的概念。掌握求函數的極值、最大值與最小值的方法,會解簡單的應用問題。

              (5)會判斷曲線的凹凸性,會求曲線的拐點。

              (6)會求曲線的水平漸近線與鉛直漸近線。

              (7)會作出簡單函數的圖形。

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