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                深圳智學學習網 - 輕松學習拿文憑從此開始!深圳積分入戶考證快速加分!

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                2016年成人高考專升本《高等數學》必背資料(2)

                時間:2015-12-30 10:32:29作者:深圳智學學習網

                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

                ()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。

                ()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(LHospital)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


                (責任編輯:馬老師 )

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