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            復習指導(2)-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(2)

            (三)連續

              1、知識范圍

              (1)函數連續的概念

              函數在一點處連續的定義、左連續與右連續函數在一點處連續的充分必要條件、函數的間斷點及其分類

              (2)函數在一點處連續的性質

              連續函數的四則運算、復合函數的連續性、反函數的連續性

              (3)閉區間上連續函數的性質

              有界性定理、最大值與最小值定理、介值定理(包括零點定理)

              (4)初等函數的連續性

              2、要求

              (1)理解函數在一點處連續與間斷的概念,理解函數在一點處連續與極限存在的關系,掌握判斷函數(含分段函數)在一點處的連續性的方法。

              (2)會求函數的間斷點及確定其類型。

              (3)掌握在閉區間上連續函數的性質,會用介值定理推證一些簡單命題。

              (4)理解初等函數在其定義區間上的連續性,會利用連續性求極限。

              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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