高等数学微积分65广义积分初步课件

1、1xOyxeyxOy21211241xy2 babdxxflim ,adxxf adxxf babdxxflim adxxf adxxf dxxf adxxf adxxf bdxxf baadxxflim30dxex0dxexbxbdxe0lim11limlim0bbbxbeexOyxey xFFxlim xFFxlim adxxf aFFxFa bdxxf FbFxFb4.12 xdx 21xdx 021xdx 021xdx 0211limaadxx bbdxx0211lim 0arctanlimaax bbx0arctanlim aaarctanlim bbarctanlim .22 5.

2、 )0,(0 ppdttept且且是常数是常数 0dttept 0dttept 01pttdep 01dtepeptptpt 0201ptptepept)10(10lim12 ptepptt.12p 6,11dxxp1p11dxx1lnx0lnlimxx1p11dxxp1111111ppppxp;11p7dxxx21021dxxx022121121xdx021x,11lim2xxdxxx21.012dxxx21xx8 ,limxfax badxxf0lim .badxxf babadxxfdxxf)(lim0)2( badxxf badxxf )lim(lim0 xfdxxfdxxfbxbab

3、a )lim(xfdxxfdxxfdxxfbcacxbccaba 3 badxxf9.41202dxx20241dxx0202arcsinx.202arcsinlim02xxxOy21211241xy10dxx1021dxx10211001limx1lim10dxx1021dxx1121dxx1121111x2dxx1121dxx0121dxx1021dxx1021dxx112111)0()(01tdxextxt0) 1(dxextxt0 xtdex00|txxtdxeex010dxxettx)(tt1) 1 (00 xxedxe又!) 1 (123) 1() 1(nnnn12Nnssntss

4、sttstssststt,2 , 1 , 2),() 1()2)(1(2 , 1 ),()2 , 1 (, 110),(1)()25(212105 . 1042dueudxexux66465. 0)5 . 1 (43)23(232113 dxxf)( bdxxf)( adxxf)( cabcbadxxfdxxfdxxf)()()( badxxf)(14dxxxdxx 124221)2(;1)1(202121)2( ;)1 () 1 (xxdxxdx2)(lnkxxdx15dxxxdxx 124221)2(;1)1(解解dxxbb 141lim)1( 式式bbx13|31lim )11(31li

5、m3bb .31 dxx 1)1(1)2(2式式 | )1arctan(x)2(2 . 16202;)1 () 1 (xdx 212102)1()1()1(xdxxdx式式解解 1020102)1(lim)1(xdxxdx因为因为 100|11limx )11(lim0 发发散散反反常常积积分分故故 202)1(xdx17211)2(xxdx解解dxxx 21111)2(式式 2121111dxxdxx212123|12|)1(32 xx.38232 182)(lnkxxdx解解 2)(lnkxxdx 2)(ln)(lnkxxd 1,)(ln1(11,| )ln(ln212kkkkxk 1,)2)(ln1(11,1kkkk时广义积分收敛于当广义积分发散时当故1;,1,kk.)2)(ln1(11 kk19,)2)(ln1(1)(1 kkkf设设又又2lnln)2)(ln1()2(ln)2(ln)1(1)(1112 kkkkkkf2lnln)1(12ln)1(12 kk, 0)( kf令令2l