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            一元函數微分學-2019年高等數學二-福建專升本

            福建成人高考信息網www.laiwobuy.com 發布時間: 2018年12月16日



            (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可導與連續的關系


            (2)導數的四則運算法則與導數的基本公式


            (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


            (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,會用定義求函數在一點 處的導數。


            (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、四則運算法則以及復合函數的求導方法。


            (4)掌握隱函數的求導法與對數求導法。會求分段函數的導數。


            (5)了解高階導數的概念,會求簡單函數的高階導數。


            (6)理解微分的概念,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)導數的應用


            1.知識范圍


            (1) 洛必達(L′Hospital)法則


            (2) 函數增減性的判定法


            (3) 函數極值與極值點最大值與最小值


            (4) 曲線的凹凸性、拐點


            (5) 曲線的水平漸近線與鉛直漸近線


            2.要求


            (1)熟練掌握用洛必達法則求“


            0 ∞ ” “ ” “0∞” “∞—∞”型未定式的極限的方法。 0 ∞


            (2)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,會利用函數的增 減性證明簡單的不等式。


            (3)理解函數極值的概念,掌握求函數的駐點、極值點、極值、最大值與最小值的方法, 會求解簡單的應用問題。


            (4)會判定曲線凹凸性,會求曲線的拐點。


            (5)會求曲線的水平漸近線與鉛直漸近線。


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