高數(shù)函數(shù)圖形的描繪

1、2xy 12222byax0byaxLbxkyNMOxyC)(xfy POxy,)(limbxfx)(xfy .by )(x或,)(lim0 xfxx)(xfy .0 xx )(0 xx或211xy2)211(limxx2 y,)211(lim1xx1 xyxO21有則曲線)(xfy .bxky)(x或,0)(limxfx)(bxk 0)(limxbkxxfxx0)(limxfx)(bxk 0)(limxbkxxfx)(limxbxxfkxxxfkx)(lim)(limxkxfbx)(x或)(x或3223xxxy,) 1)(3(3xxxy,lim3yx) 1(x或3x1xxxfkx)(lim3

2、2lim22xxxx1)(limxxfbx3232lim22xxxxx22xy312 xyyxO)(xfy , )(, )(xfxf )(xf )(xf 22331xxy, ),(,22xxy,22 xy,0 y令2,0 x得,0 y令1x得xyy y012)0,() 1 ,0()2, 1 (),2(0023432xy1332201123yOx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(2xxy定義域?yàn)槎x域?yàn)?, 1 ( , ) 1 ,(2) 求關(guān)鍵點(diǎn)求關(guān)鍵點(diǎn).)3(2xy4044yxy) 1(223xyxy2) 1(4) 1)(3(xxxy

3、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(dǎo)得求導(dǎo)得兩邊對兩邊對 x 求導(dǎo)得求導(dǎo)得113) 1,() 1 , 1()3, 1 (), 3(xyy y20,) 1(4)3(2xxy,) 1(4) 1)(3(2xxxy3) 1(2 xy00,lim1yx1xxyxlim,4141k)41(limxybx41) 1(4)3(lim2xxxx) 1(495limxxx45) 1(4)3(2xxyxy0492414541xy2) 1(4) 1)(3(xxxy3) 1(2 xy1x4541xy2xy113) 1,() 1 , 1()3, 1

4、 (), 3(0 xy04924112Oyx3215) 1( 4) 3(2xxy1x4541xy21y22ex, ),( y21,e22xx y2122ex)1 (2x得令0 y;0 x得令0 y1x2100e21xyy y10) 1,0(), 1 (0limyx0y2100e21xyy y10) 1,0(), 1 (22e21xyxyOA210yB1水平漸近線水平漸近線 ; 垂直漸近線垂直漸近線; 內(nèi)容小結(jié)內(nèi)容小結(jié)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(jìn)行按作圖步驟進(jìn)行2. 函數(shù)圖形的描繪函數(shù)圖形的描繪)(e1e122xxy;1e1e1lim22xxx22e1e1lim0 xxxD),(21)e1,(21212e1xy)21 (e222xyx ),(2121),(211yyOx1)e1 ,(2121)e1 ,(2121yxayx333x,133ttay233,1att, 1tx時(shí)當(dāng)xyxlim1limt3213tta313tta1)(limxyx1limt3213tta313tta)1)(1 ()1 (