數(shù)學分析歷年競賽題PPT課件

1、dxxxxex2cos)cossin1 ()2010(. 1求年1競賽題dxxxedxxedxxxxexxxcossincoscos)cossin1 (:22解dxxexdexxtan)(tandxxeexdxexxxtan)(tantandxxedxxexexxxtantantan.tanCxex第1頁/共19頁dxxxx1)2009(. 2求年2競賽題,2,:2tdtdxtxtx ，則設解tdtttdxxxx2113dttt3212 )1 (113233tdt.CxxCt1341343 第2頁/共19頁3競賽題 dxxxxx)cos(sinsincos. 3 求dxxxxxxx)cos(s

2、insinsin)sin(cosdxxsin1dxxxcossin1dxxxxx)cos(sinsincos解：第3頁/共19頁4競賽題 dxxsin1dxxxcossin1|cotcsc|lnxx dxx)4sin(121 Cxx| )4cot()4csc(|ln21|cotcsc|lnxx 第4頁/共19頁5競賽題 dxxxxsin4cos3sin. 4 求dxxxxIsin4cos3sin:解dxxxxxxsin4cos3cos4)cos4sin3(31dxxxxxsin4cos3cos4sin331dxxxxsin4cos3cos34第5頁/共19頁6競賽題 dxxxxxsin4cos

3、3cos4sin331dxxxxsin4cos3cos34xxxxdsin4cos3)sin4cos3(31dxxxxxxsin4cos3sin4)sin4cos3(94|sin4cos3|ln31xxdx194dxxxxsin4cos3sin916|sin4cos3|ln31xxIx91694第6頁/共19頁7競賽題|sin4cos3|ln31xxI因為,91694Ix CxxxI)94|sin4cos3|ln31(259所以Cxxx254|sin4cos3|ln253第7頁/共19頁8競賽題dxxxxx)1 (1. 5884求dxxxxx)1 (1:884解dxxxxxx)1 ()2()1

4、 (8488dxxxxx)121(837dxxxdxxxdxx83871121第8頁/共19頁9競賽題dxxxxxxxddxx)11(211)1 (81214343884444881)1 (41211)1 (41)21(1)1 (411xxdxxdxxddxx |ln x|1 |ln418x|1 |ln814xCx|1 |ln814|ln x|1 |ln418xCxx|11|ln8144dxxxdxxxdxx83871121第9頁/共19頁10競賽題dxxxxx23)1ln()2ln(. 62求dxxxxx) 1)(2()1ln()2ln(dxxxxx2111)1ln()2ln(dxxxxx1

5、121)1ln()2ln(dxxxxx23)1ln()2ln(:2解第10頁/共19頁11競賽題)1ln()2ln()1ln()2ln(xxdxxCxx2)1ln()2ln(21dxxxxx1121)1ln()2ln(第11頁/共19頁12競賽題dxxx1. 759求dxxx1:59解151555xdxxux 5令151uududuuu11) 1(51 duuu11151第12頁/共19頁13競賽題 duuu11151) 1() 1(5121udu) 1() 1(5121udu121) 1(3251uCu121) 1(2515xu 回代Cxx152) 1(1525235第13頁/共19頁14d

6、xexxxx1)11 (. 8求dxexxxx1)11 (所以，Cxexedxxxx11)(競賽題)()(111xxxxxxexexxe因為)11 (211xxeexxxxxxexx1)11 (方法一解:第14頁/共19頁15dxexxxx1)11 (. 8求dxexxxx1)11 (:方法二解dxexx1dxexxxx1)1(dxexxxdexexxxxxx111)1()(競賽題dxexxdxexxxexxxxxx1121)1()11 (Cxexx1第15頁/共19頁16dxxx32sin. 9求33sin31dxxdxxx32sin:解ux 3令udusin31Cu cos313xu 回代Cx 3cos31 競賽題第16頁/共19頁171.102xxdx求，則令tx12tdtdx 方法一解:12xxdx111122ttdtt222111ttdttCttdtarccos12Cx1arccos競賽題第17頁/共19頁181.102xxdx求方法二解:，則令txse