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Модуль 7. Нескінченно малі і нескінченно великі функції5)6)7)x a x a2 cos x a x asin , x a lim 2 22 2x ax ax a lim cos cos a.x a22(1 cos x)1 cos(1 cos x) 0 1 cos(1 cos ) ,lim x 042xx 0 1 cos x 0, x 0 2x 22x(1 cos ) 1 cos , 2 x x 1 lim lim .0 4 2 x 0 42xxx 02x8ln(1 5 x) 0 ln(1 5 x) 5 x,5xlim lim 5.x 0 x 0xx0 x0xln(1 3 ) 3 ,xxln(1 3 ) 0 x x 3lim ln(1 2 ) 2 , lim xln(1 2 ) 0 xx 2x xx28)9) 3xe 3lim 0. 2 x3xe 1 0 1 3 x,3xlim lim 3.x 0 x 0xx 0 x 0sin 5x sin x sin x sin 5xsinx3 3 0 3 (3 1)lim limcos 0xe x ( e 1) (1 cos x)x0 xx0sin 5xsinx sin x3 1 (sin 5x sin x)ln 3 2e ln 3 sin 2x cos 3x lim 2 ln 3 sin 2x cos 3 x, x 0 x0x( e 1) (1 cos x)xsin x3 1, cos 3 1,sin x sin 2x x 2eln 3 cos 3xxsin 2 1lim xx e 2, 1, 4 ln 3.x 0xe 1 1 cosxx x 1 cosx 0, x 0x x10)1 5 1x 0 (1 x) 1 x,xlim 5 lim 5.1 x 1 0 x 01x5x0 5x0