高数函数图形的描绘-文档资料

1、122xy 12222byax0byaxLbxkyNMOxyC)(xfy POxy3,)(limbxfx)(xfy .by )(x或,)(lim0 xfxx)(xfy .0 xx )(0 xx或211xy2)211(limxx2 y,)211(lim1xx1 xyxO214有则曲线)(xfy .bxky)(x或,0)(limxfx)(bxk 0)(limxbkxxfxx0)(limxfx)(bxk 0)(limxbkxxfx)(limxbxxfkxxxfkx)(lim)(limxkxfbx)(x或)(x或53223xxxy,) 1)(3(3xxxy,lim3yx) 1(x或3x1xxxfkx)

2、(lim32lim22xxxx1)(limxxfbx3232lim22xxxxx22xy312 xyyxO6)(xfy , )(, )(xfxf )(xf )(xf 722331xxy, ),(,22xxy,22 xy,0 y令2,0 x得,0 y令1x得xyy y012)0,() 1 ,0()2, 1 (),2(0023432xy1332201123yOx8例例4. 描绘方程描绘方程044)3(2yxyx的图形的图形.解解: 1),) 1(4)3(2xxy定义域为定义域为), 1 ( , ) 1 ,(2) 求关键点求关键点.)3(2xy4044yxy) 1(223xyxy2) 1(4) 1)

3、(3(xxxy 42048 yxy) 1(241 xyy3) 1(2x得令0 y;3, 1x原方程两边对原方程两边对 x 求导得求导得两边对两边对 x 求导得求导得9113) 1,() 1 , 1()3, 1 (), 3(xyy y20,) 1(4)3(2xxy,) 1(4) 1)(3(2xxxy3) 1(2 xy00,lim1yx1x10 xyxlim,4141k)41(limxybx41) 1(4)3(lim2xxxx) 1(495limxxx45) 1(4)3(2xxyxy0492414541xy2) 1(4) 1)(3(xxxy3) 1(2 xy111x4541xy2xy113) 1,

4、() 1 , 1()3, 1 (), 3(0 xy04924112Oyx3215) 1( 4) 3(2xxy1x4541xy1221y22ex, ),( y21,e22xx y2122ex)1 (2x得令0 y;0 x得令0 y1x2100e21xyy y10) 1,0(), 1 (130limyx0y2100e21xyy y10) 1,0(), 1 (22e21xyxyOA210yB114水平渐近线水平渐近线 ; 垂直渐近线垂直渐近线; 内容小结内容小结1. 曲线渐近线的求法曲线渐近线的求法斜渐近线斜渐近线按作图步骤进行按作图步骤进行2. 函数图形的描绘函数图形的描绘15)(e1e122xxy;1e1e1lim22xxx22e1e1lim0 xxxD16),(21)e1,(21212e1xy)21 (e222xyx ),(2121),(211yyOx1)e1 ,(2121)e1 ,(21211718yxayx333x,133ttay233,1att, 1tx时当xyxlim1limt3213tta313tta1)(limxyx1limt3213tta313tta)1)(1 ()1 (312limtttttata