高數函數圖形的描繪ppt課件

1、11/5/2021111/5/202122xy 12222byax0byaxLbxkyNMOxyC)(xfy POxy11/5/20213,)(limbxfx)(xfy .by )(x或,)(lim0 xfxx)(xfy .0 xx )(0 xx或211xy2)211(limxx2 y,)211(lim1xx1 xyxO2111/5/20214有則曲線)(xfy .bxky)(x或,0)(limxfx)(bxk 0)(limxbkxxfxx0)(limxfx)(bxk 0)(limxbkxxfx)(limxbxxfkxxxfkx)(lim)(limxkxfbx)(x或)(x或11/5/2021

2、53223xxxy,) 1)(3(3xxxy,lim3yx) 1(x或3x1xxxfkx)(lim32lim22xxxx1)(limxxfbx3232lim22xxxxx22xy312 xyyxO11/5/20216)(xfy , )(, )(xfxf )(xf )(xf 11/5/2021722331xxy, ),(,22xxy,22 xy,0 y令2,0 x得,0 y令1x得xyy y012)0,() 1 ,0()2, 1 (),2(0023432xy1332201123yOx11/5/20218例例4. 描繪方程描繪方程044)3(2yxyx的圖形的圖形.解解: 1),) 1(4)3(2

3、xxy定義域為定義域為), 1 ( , ) 1 ,(2) 求關鍵點求關鍵點.)3(2xy4044yxy) 1(223xyxy2) 1(4) 1)(3(xxxy 42048 yxy) 1(241 xyy3) 1(2x得令0 y;3, 1x原方程兩邊對原方程兩邊對 x 求導得求導得兩邊對兩邊對 x 求導得求導得11/5/20219113) 1,() 1 , 1()3, 1 (), 3(xyy y20,) 1(4)3(2xxy,) 1(4) 1)(3(2xxxy3) 1(2 xy00,lim1yx1x11/5/202110 xyxlim,4141k)41(limxybx41) 1(4)3(lim2x

4、xxx) 1(495limxxx45) 1(4)3(2xxyxy0492414541xy2) 1(4) 1)(3(xxxy3) 1(2 xy11/5/2021111x4541xy2xy113) 1,() 1 , 1()3, 1 (), 3(0 xy04924112Oyx3215) 1( 4) 3(2xxy1x4541xy11/5/20211221y22ex, ),( y21,e22xx y2122ex)1 (2x得令0 y;0 x得令0 y1x2100e21xyy y10) 1,0(), 1 (11/5/2021130limyx0y2100e21xyy y10) 1,0(), 1 (22e21

5、xyxyOA210yB111/5/202114水平漸近線水平漸近線 ; 垂直漸近線垂直漸近線; 內容小結內容小結1. 曲線漸近線的求法曲線漸近線的求法斜漸近線斜漸近線按作圖步驟進行按作圖步驟進行2. 函數圖形的描繪函數圖形的描繪11/5/202115)(e1e122xxy;1e1e1lim22xxx22e1e1lim0 xxxD11/5/202116),(21)e1,(21212e1xy)21 (e222xyx ),(2121),(211yyOx1)e1 ,(2121)e1 ,(212111/5/20211711/5/202118yxayx333x,133ttay233,1att, 1tx時當xyxlim1limt3213tta313tta1)(limxyx1limt3213tta313tta)1)(