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# sol_first_term - '` cren oexzt 104281 2 itpi` 1 dl`y ` sirq...

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Unformatted text preview: '` cren oexzt - 104281- 2 itpi` 1 dl`y ` sirq llkend lxbhpi`d α ikxr eli` xear Z 1 dx (1- cos x ) α ?xcazn `ed α ikxr el` xeare ,qpkzn :oexzt g ( x ) = divwpetd mr d`eeyd ogan rval lkep okle [0 , 1] megza ziaeig f ( x ) = 1 (1- cos x ) α divwpetd :`ad leabd z` wecap okl qt` zaiaqa dneqg dpi` f ( x ) divwpetd . 1 x 2 α lim x → + f ( x ) g ( x ) = lim x → + x 2 α (1- cos x ) α =     lim x → + x 2 1- cos x | {z } =2 lhitel i"r     α = 2 α > qpkzn R 1 g ( x ) dx lxbhpi`d .cgia mixcazne miqpkzn R 1 g ( x ) dx-e R 1 f ( x ) dx milxbhpi`d okle . α < 1 2 m"m` qpkzn R 1 f ( x ) dx lbhpi`d okle 2 α < 1 m"m` a sirq :mixcazn e` miqpkzn mi`ad millkend milxbhpi`d m` raw Z ∞ 1 | arctan x | x dx, Z ∞ 1 x 6 e x dx :oexzt :`ad aeyigd t"r R ∞ 1 1 x dx xcaznd lxbhpi`d mr d`eeyd i"r xcazn R ∞ 1 | arctan x | x dx lim x →∞ | arctan x | x 1 x = lim x →∞ | arctan x | = π 2 > . [1 , ∞ ) megza zeiaeig | arctan x | x mbe 1 x mb ik d`eeydd ogana ynzydl ozipy al miype miiaeig micp`xbhpi`d dt mb) R ∞ 1 1 x 2 dx qpkznd lxbhpi`d mr d`eeyd i"r qpkzn R ∞ 1 x 6 e x dx ( ∞- l mit`ey dpknde dpend) oexg`d alya lhitel llka xfrpy `ad aeyigd i"r (megza lim x →∞ x 6 e x 1 x 2 = lim x →∞ x 8 e x = 0 1 2 dl`y i"r zxcben f ( x,y ) idz f ( x,y ) = (...
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sol_first_term - '` cren oexzt 104281 2 itpi` 1 dl`y ` sirq...

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