2019第一学期高等数学期末复习ppt课件

1、321221xxxlimx62222xxxxlimx321221xxxlimx31111xxxxlimx311xxlimx31114221321221xxxlimxxxxlimx 32 12212221xxlimx222422162222xxxxlimx32122xxxxlimx312xxlimx32125362222xxxxlimxxxxxlimx 6 222212122xxlimx12212253324322xxxxlimx2321422xxxlimx324322xxxxlimx22312413xxxxlimx00200323324322xxxxlimxxxxxlimx 32 432223

2、1416xxlimxxxlimx 14 1646xlim2321422xxxlimx2223214xxxlimx0020422321422xxxlimxxxxlimx 232 1422348xxlimxxxlimx 34 848xlim2xtanxsinlimx320 xsinxlimx422010 xxsinlimxxtanxsinlimx320 xxlimx32032xtanxsinlimx320 xtanxsinlimx 3 20 xxsecxxcoslimx 33 2220 xsecxcoslimx332220131232xsinxlimx4220 xxlimx422020 xlimx

3、0 xsinxlimx4220 xsinxlimx 4 220 xxcosxlimx 4440 xcosxlimx444014040exlimxx11xxxlim1021xxxlim301exlimxx101xxxlim1021xxxlim2102122exxxlim301xxxlim10133 e31eexlimxx11xxxlim21xxxlim231xxxlim21221xxxlim22 e21exxxlim231331xxxlim66e xf， 1xe， 1， 2x0 x0 x0 x 0f xflimx0 xflimx0 xflimx00 x xf xf， 1xe， 1， 2x0 x0

4、 x0 x xflimx0 xflimx0 00 xflimx0 x xf 10 f10 xxelim10 e0 xlimx20020 xflimx0 xflimx00， 1xe0 x， 2x0 x 10 f 00 xflimx 00fxflimx 1f xflimx1 xflimx1 xflimx11x xf xf， 11x， 1， 1313xx1x1x1x 1f xflimx1 xflimx1 21xflimx xf， 11x， 1， 1313xx1x1x1xx111x1313xx1x11xxlimx111111213131xxlimx1313242 xflimx1 xflimx121x

5、xf 11 f 21xflimx 11fxflimx1 xflimx 0 xflimx12xx x11xexe12xlnxcosxsin10120 xxlimxxlimx110100eelimxx010 xxelimxxelim10 xxelim1020 xlnlimxxcosxsinlimx10 xcosxsinlimx 1 0 xsinxcoslimx05212xxxy3422xxxy522 xx412 x0 ,0342 xx02 x2x1x3x 3 , 3 2 ,3xxexxy213 y 1 y5cosxlnxy y 1 yxexxy213，求 y 1 yxexx y21 3 exxx

6、2 13xexx213221 xx 233 xx211 xx xxee e y2131 e225cosxlnxy y 1 y5 cosxlnx y0121xxxx121xx22 11211 y2312121 xxxxln1 x21xcosxsiny2，求dy 0 yxcosxsin y 2 dx ydy 0 y xcosxsin 2 xsinxxcos 22xsinxcos22002sincos0122dxxsinxcos 22xcosxsin xsinxcos dx ydy 321xcosy，求dy 0 y321 xcos ydxxcosxsin2216 xcosxcos 212132xsi

7、nxcos2021322216xcosxsin 2021060 cossin y0dx ydy xsinxcos dx ydy dxdududydxdy 233 uuxcosxsiny1y 6 yxcosxsin y1 21 11 xcosxcosxsinxcosxsin2101xcosxsinxsinxcosxcosvu 2 vuvvu6 y2221 xcosxsinxcosxcos y211xcosxcosxcos11611cos2311322322y 21 1xcosxcos2 uuu1210 xcosxsinxcos1121xcosxsinxxeey1和y 0 y y xxee1 21

8、 11 xxxxxeeeee2101xxxxxeeeee2221xxxxeeee21xxeevu 2 vuvvu2001 ee 0 y211141y 21xxee 422111 xxxxxeeeee421 1121xxxxxxeeeeeey 31021xxxxxeeeee32212xxxxeeee321xxxeee311xxxeeexlny1，求dy y y yxln1211xlnxln 121xln 121xx 1112110121x121xdydx y dxx 121dydx y uln u11442xxlnydy y y y1442xxln212 xln122xln122xlnxx 12

9、121202122x124xdydx y dxx124dydx y uln u1 xfy 12223yyxxdxdy 1 2223yyxx 0 2 223yyxx 0 2 23222yyyxyxx0 2 22322yy yxxyx0 2 24322yy yxxyxxyx yyx43 2222 y yxxyx224322dxdy xfy 1322yxyxdxdy 1 322yxyx 0 322yxyx 0 3 2222 yyyxyxx0 3 2222 yyyyxyx0 3 2222 yyxyyyx222 32yx yyxy y 22322yxyyxdxdy0 xxexy 3 y xex 3xe3

10、 0 y03e132切线k 0 y20 xy003e1 1 0 ,021xy12 xy00 xxkyy切线k 0 x yxlnxy12 xy y 11 ln切线k21x121xy12 xy00 xxkyy切线k 0 x y y,x直线kxlnxx11211xy1 ,133xxy y xx 133332 x0 y1xx 1 ,1 1 1 ,1 1 , y 00y31 1 , 1 , 1 1 ,31 y 11y1x1x ,1224xxy y xx 1224xx4430 y11x02x13xx 1 ,1 0 1 ,1 1 , y 0y0001 1 0 ,00 1 , 1 , 0 1 , 10 y01

11、 y0 x1x 1 0 ,1x 01 yx33 ,3333 33,33 33,y 00y9494 1 , 1 , 1 1 ,31 y 11y1x1x xfxF xF xf xF xf CxF xf CxFdxxf dxxf xf dxxfd dxxf dxdxxf CxFdxxF CxFxdF复习题三、16复习题三、15kdxxdxx x dx 2xxdx2xdxdxkCxCx111Cx 221Cx 211xx2Ckxx1xxdxx23xdxxx232123x1xCx111Cx 2332dxx1Cx 2xx2121xdxx1Cxln xlnx1 xedxexxcosxdxsinxsinxeCe

12、xCxcosxdxcosCxsinxsinxcosdxx211Cxarctanxarctan211xdxexxdxsinCexCxcosxdxcosCxsindxx211CxarctandxxdxxdxCxCx111Cx 221dxxCx 2332dxx1Cx 2dxx1Cxln 其次考虑幂函数 第11题、第12题dxlnxcosx321dxlnxdxcosdxx321Clnxxsinx322dxlnxcosx321Cxdxx21CxsinxdxcosCxdxdxxsinexxx3212Cxlndxx 1CxcosxdxsinCedxexxdxxsinexxx3212xdxsindxedxxx

13、x3212xcosedxxxx321Cxcosexxlnx3221 2Cxxdx221dxxx5232222dxxdx Cuduu6561dxxx52322xdxx2325225232dxx 252323231xdxCx62326131xdx22dxCx6232181dxxx223221dxxdx Cuduu2332dxxx223xdxx223222321dxxxdx2dx212223232121xdxCx232233241Cx2322361dxeexx23xxdedxeCulnduu 1dxeexx23dxeexx231xxdee231xxede2323121Celnx2321dxexxde

14、dxeexx21xxdedxexxdee21xxede212121Cex23213221dxeexx21dxeexx21dxexxdeCex232131Cuduu2332dxxsinxcos2xsindxdxcosCulnduu 1dxxsinxcos2xdxcosxsin21xsindxsin21xsindxsin221Cxsinln2xdxcosxsinddxxcosxsin23xcosdxdxsinCuduu2332xcosdxcos23xcosdxcos232321Cx23cos233221dxxcosxsin23xdxsinxcos23xdxsinCx23cos2331xcosd x

15、f， 2x0 x0 x， 1 1 1 dxxf 0 1 dxxf0 1 1 dxxf2201 1 0 dxxf1000 1 1dx1 0 2xdx0 1 x1 0 2x2CxdxCxxdx22dxxdx2x2x0 xx20 x1 3 0 dxxf220121011 0 1dxx3 1 1dxx1 0 x1 0 221x xf， 1x1x1x， 1x 3 0 dxxf 1 0 dxxf 3 1 dxxf3 1 x3 1 221x1322132121edxxlnx 1 2 3231dxdxxdxxxlnd1edxxlnx 1 2 edxxxln 1 2dxx2edxxln 1 3 31313dxe

16、exlndxxlnx 1 3 1 3 31bababavduvuudv eexlndxxlnx 1 3 1 3 edxxxlnelne 1 331131dxx1xlndedxxe 1 23031exe 1 33313191923e1 0 2dxxexdxex21 0 2dxxex1 0 2dxexx1 0 221xxdexde2211 0 21 0 221dxexexxbaudv 1 0 22221021xdeexxdex2212bavu bavdu 1412122ee41412e1412edxex221xde21 0 21 0 2dxexexx1 1 33 dxxsinx 33xsinxxf

17、33xsinxxf33xsinx xf 33xsinxxf0 1 1 33dxxsinx1 1 2 11dxxxsin1 1 2 11dxxxsin1 1 21 1 2 1 11dxxxsindxx0 1121 0 2dxx1 0 2xarctan012arctanarctan 422xe3 xf dxxfd xe3 xf xfex 3xex 33xe33 dxxfd dxxfdxex33xe3 xf dxxfd xe3 xf dxxfCex3 dxxfd dxex33dxex 3 Cxcosdxxf2 dxxf xf xfxcos2xxsin22xsin22dS dxxf dxx 22S2

18、0 dS2 0 2 2 dxx xfh 2 0 2 0 3231xx438320326dS dxxf dxxx 222S2 0 dS2 0 2 22dxxx xfh 2 0 2 0 22 0 3231xxx443838322Cxxdx221CxsinxdxcosCxdxx3231xsinxy 6 xsinxy 6 dxxsinx y6 123CxcosxdxCxcosxy 312213CxCxsinxCxcosxdxsin23xx6dxxcosxsindx23xdx3xxcosdxxsinCxdxx3231Cxxdx221Cxdxx4341dxx y 212 21324CxxCxdx34x212xdxx22dx212 2xy212 2xy 10 y 00 y