? E 1c° ú=) ? x1 ? ? ????))) ? ? ?DDD°°° ú ú ú===))) ? ? ? 1￡ ü (1) sinxsin2x￠￠￠sinnx￠￠￠ ^[0;…] ￥??" (2) sinxsin3x￠￠￠sin(2n+1)x￠￠￠ ^[0; …2] ￥??" (3) 1cosxcos2x￠￠￠cosnx￠￠￠ ^[0;…] ￥??" (4) 1sinxsin2x￠￠￠sinnx￠￠￠? ^[0;…] ￥??" 2 p/ ? ù12…￥f ?￥° ú=) ? (1) ??[ TPn (x) = nP i=0 (ai cosix+bi sinix) (2) f (x) = x3 (?… < x < …) (3) f (x) = cos x2 (4) f (x) = eax (?… < x < …) (5) f (x) = jsinxj (?… < x < …) (6) f (x) = xcosx (?… < x < …) (7) f (x) = 8 < : x; ?… < x < 0 0; 0 ? x < …  (8) f (x) = …2 ?x2 (?… < x < …) (9) f (x) = sgncosx (10) f (x) = …?x2 (0 < x < 2…). 1 3 !f(x)[2…1? ù[?…;…] ' V￡ ü (1) ?Tf ?f(x)[?…;…] ?@f (x+…) = f (x)5 a2m?1 = b2m?1 = 0; m = 1;2;￠￠￠ (2) ?Tf ?f(x)[?…;…] ?@f (x+…) = ?f (x)5 a2m = b2m = 0; m = 1;2;￠￠￠ : x2°°° ú ú ú===))) ? ? ?￥￥￥ l l l ? ? ???? 1|/ f ?Z?° ú=) ?i) ? l ?? (1) f (x) = xsinx x 2 [?…;…] (2) f (x) = 8 < : x2; x 2 [0;…] 1; x 2 [?…;0)  2?Z 7 T x = 2 1X n=1 (?1)n+1sinnxn (?… < x < …) (1)¨?[sE px2x3x4(?…;…)?￥° ú=Z 7 T (2) p) ?1P n=1 (?1)n+1 n4 1P n=1 1 n4￥?. 3(1)(?…;…) = pf (x) = ex￥° ú=Z 7 T (2) p) ?1P n=1 1 1+n2￥?. 4 !f(x)[?…;…] ? V± Of (?…) = f (…). anbn1f(x)￥° ú=" ?a0nb0n ^f(x)￥?f ?f0(x)￥° ú=" ?￡ ü a00 = 0a0n = nbnb0n = ?nan ( n = 1;2;￠￠￠): 2 5￡ ü ? ??) ? a0 2 + 1X n=1 (an cosnx+bn sinnx) ?￥" ?anbn ?@1" max'flfln3anflfl;flfln3bnflfl“? M ?M1è ?5  ? ??) ? l ? O ?f ? μ ??￥?f ?. 6 !Tn (x) = a02 + nP k=1 (ak coskx+bk sinkx) p￡ Tn (x) = 12… Z … ?… Tn (x+t) sin ?n+ 1 2 ￠t sin t2 dt: 7 !f(x)[2…1? ù(0;2…) ???h Oμ? p￡bn ? 0 (n > 0). 8 !f(x)[2…1? ù(0;2…) ? ?f0(x)??  6μ?. p ￡an ? 0 (n > 0). 9￡ ü ?f(x)x0? ?@fi¨￥ ? ?GHq5f(x)x0? ??. óB?V ü? ?￥ I 5?? ?￥ è0. 10 !f(x) ^[2…1? ù￥f ?[?…;…] ' V? !Sn (x) ^f(x)￥° ú=) ?￥ -n[?s? Sn (x) = a02 + nX k=1 (ak coskx+bk sinkx) 5Sn (x) = 4… R … 20 f(x+2t)+f(x?2t) 2 Dn (2t)dt ?Dn (t) ^3 ? X ??. 11 !f(x) ^[2…1? ù(?1;1) ?? ?￥° ú=) ?x0? l ?. p￡ Sn (x0) ! f (x0) (n ! +1): 3 12 !f(x) ^[2…1? ùa ?? ° ú=" ? ?105f (x) · 0. 13 !f(x) ^[2…1? ù[?…;…] ' V.? !x0 2 (?…;…) ?@ lim t!0+ f (x0 +t)+f (x0 ?t) 2 = L i.￡ ülimn!1 n (x0) = L.éB? ?f(x)x0? ??5limn!1 n (x0) = f (x0) ? n (x) = 1n+1 nX k=0 Sk (x): x3 ? ? ?iii u u uWWW   ￥￥￥°°° ú ú ú===))) ? ? ? 1|/ f ?·? uW Z 71° ú=) ?i) ?  l ?? (1) uW(0;2l)Z 7 f(x) = 8 < : A; 0 < x < l; 0; l ? x < 2l; (2) f(x) = xcosx; ??…2; …2￠ (3) f(x) = x; (0;l) (4) f(x) = 8 >>> < >>> : x; 0 ? x ? 1; 1; 1 < x < 2; 3?x; 2 ? x ? 3: 2 p/ ? ùf ?￥° ú=) ? (1) f(x) = jcosxj (2) f(x) = x?[x]. 3ü/ f ?·? uW Z 71??) ? 4 (1) f(x) = sinx; 0 ? x ? … (2) f(x) = 8 < : 1?x; 0 < x ? 2; x?3; 2 < x < 4: 4ü/ f ?·? uW Z 71??) ? (1) f(x) = cos x2; 0 ? x ? … (2) f(x) = x2; 0 ? x ? 2. 5üf ?f(x) = (x?1)2(0;1) Z 7???) ?iw …2 = 6 1+ 122 + 132 +￠￠￠ ? : 6|f ?f(x)sYT ü?? }ü?a pf ?￥° ú=) ?  ? f(x) = 8 >>> < >>> : 1; 0 < x < …2; 1 2; x = … 2; 0; …2 < x ? …: 7?? ??üó? uW?0; …2￠￥ Vf ?ü?? uW(?…;…) = P ¤ ?(?…;…)??￥° ú=) ?1 (1) f (x) ? 1P n=1 a2n?1 cos(2n?1)x (2) f (x) ? 1P n=1 b2n?1 sin(2n?1)x. x4°°° ú ú ú===))) ? ? ?￥￥￥ ü ü ü ( ( ( l l l ? ? ???? 5 1 ?f(x),g(x)[2…1? ù[?…;…] üZ V f(x) ? a02 + 1X n=1 (an cosnx+bn sinnx); g(x) ? fi02 + 1X n=1 (fin cosnx+fln sinnx); 5 1 … Z … ?… jf(x)g(x)jdx = a0fi02 + 1X n=1 (anfin +bnfln): 2 !f(x)[0;l]  üZ V p￡ 2 l Z l 0 f2(x)dx = 12a20 + 1X n=1 a2n ? an = 2l Z l 0 f(x)cos n…xl dx: 6