??? E E E???cccííífff ? ? ?￥￥￥KKKDDD ? ? ??????? x1 ü ü ü ? ? ????""" 1 !fPn = (xn;yn)g ^ ü ?? P0 = (x0;y0) ^ ü ? ￥?.￡ ülimn!1Pn = P0￥ 1Hq ^limn!1xn = x0 Olimn!1yn = y0. 2. ! ü ?? fPng l ?￡ üfPngμ?. 3. ?Y/  ü ??" 't ^ 7"a>"aμ?"? u×isY·  ? ì￥ ? (1) E = '(x;y)jy < x2“ (2) E = '(x;y)jx2 +y2 6= 1“ (3) E = f(x;y)jxy 6= 0g (4) E = f(x;y)jxy = 0g (5) E = f(x;y)j0 ? y ? 2;2y ? x ? 2y +2g (6) E = '(x;y)jy = sin 1x;x > 0“ (7) E = '(x;y)jx2 +y2 = 1E = 0;0 ? x ? 1“ (8) E = f(x;y)jx;yg. 4 !F ^>"G ^ 7"￡ üFnG ^>"GnF ^ 7". 5￡ ü 7"￥?" ^>". 6 !E ^ ü ??".￡ üP0 ^E￥ ?￥ 1Hq ^E?i? fPng ?@ Pn 6= P0 (n = 1;2;￠￠￠) limn!1Pn = P0: 1 7¨ ü ? ￥μK-?? ?￡ üá á?? ?. 8¨á á?? ?￡ ü O l ?e ?. 9 !E ^ ü ??" ?T"?E￥ ?B-??μμK0-?5 ?E ^?".￡ ü?" ^μ?>". 10 !E ^ ü ? ￥μ?>"d(E) ^E￥°?' d(E) = sup P0;P002E r?P0;P00￠: p￡iP1;P2 2 E P¤r(P1;P2) = d(E). 11_v ü ??"? ?n? x f bW??"￥μ1à Q( ? #×a Ka 7"a ?a>"a u×aμ?[#Bt'? ??). 12? ?i￡ ü ?? bW￥o:3 vé: ?+ ? ?á á?? ?. x2ííífff ? ? ?￥￥￥KKKDDD ? ? ??????? 1? ?/ ?l (1) limx!x 0y!y 0 f (x;y) = 1 (2) lim x!+1 y!?1 f (x;y) = A (3) limx!a y!+1 f (x;y) = A (4) limx!a y!+1 f (x;y) = 1. 2 p/ K  ?d?èK (1) lim x!0 y!0 x2+y2 jxj+jyj (2) lim x!0 y!0 sin(x3+y3) x2+y2 2 (3) lim x!0 y!0 x2+y2p 1+x2+y2?1 (4) lim x!0 y!0 (x+y)sin 1x2+y2 (5) lim x!0 y!0 x2y2 ln?x2 +y2￠ (6) lim x!0 y!0 ex+ey cosx?siny (7) lim x!0 y!0 x2y32 x4+y2 (8) lim x!0 y!2 sin(xy) x (9) lim x!1 y!0 ln(x+ey)p x2+y2 (10) lim x!1 y!2 1 2x?y (11) lim x!0 y!0 xy+1 x4+y4 (12) lim x!0 y!0 1+x2+y2 x2+y2 (13) lim x!+1 y!+1 ?x2 +y2￠e?(x+y) (14) lim x!+1 y!+1 ? xy x2+y2 ·x2 . 3) ?/ f ?(0;0)?￥ ? ?K? ? ?QK (1) f (x;y) = x2x2+y2 (2) f (x;y) = (x+y)sin 1x sin 1y (3) f (x;y) = ex?eysin(xy) (4) f (x;y) = x2y2x2y2+(x?y)2 3 (5) f (x;y) = x3+y3x2+y (6) f (x;y) = x2y2x3+y3 (7) f (x;y) = x4+3x2y2+2xy3(x2+y2)2 (8) f (x;y) = x4y4(x2+y4)3. 4? ?i￡ ü=íf ?K￥ ?μ??? ?? ? |?? ?. 5? ?i￡ ülimx!x 0y!y 0 f (x;y)i￥ O l ?5. 6 kTf ?f (x;y) P?(x;y) ! (x0;y0) H (1) ? ?K? ? ?QK??i (2) ? ?K?i ? ?QKi??M? (3) ? ?K? ? ?QK?i. 7) ?/ f ?￥ ??S? (1) f (x;y) = 1px2+y2 (2) f (x;y) = 1sinxsiny (3) f (x;y) = [x+y] (4) f (x;y) = x+yx3+y3 (5) f (x;y) = 8< : sin(xy) y ; y 6= 0; 0; y = 0; (6) f (x;y) = 8< : sin(xy)p x2+y2; x 2 +y2 6= 0; 0; x2 +y2 = 0; 4 (7) f (x;y) = 8 < : 0;x1í ? ? y;x1μ ? ?  (8) f (x;y) = 8 < : y2 ln?x2 +y2￠; x2 +y2 6= 0; 0; x2 +y2 = 0; (9) f (x;y) = 8< : x (x2+y2)p; x 2 +y2 6= 0; 0; x2 +y2 = 0; (p > 0). 8 ?f (x;y)  u×G =M x ??M y ?@ ? ?GH q' ?i ?x;y0￠2 G?x;y00￠2 Gk flflf ?x;y0￠?f ?x;y00￠flfl? Lflfly0 ?y00flfl ?L1è ? p￡f (x;y)G = ??. 9￡ üμ?>" =í ??f ?￥K′? ??Bá ???? ?. 10 !=íf ?f (x;y) ? ü ?  ??lim x2+y2!1 f (x;y) = A p ￡ (1) f (x;y) ? ü ?μ? (2) f (x;y) ? ü ?Bá ??. 11￡ ü ?f (x;y)sY ?BM x?y ^ ??￥i O ?￥B ? ^??￥5f (x;y) ^=í ??f ?. 12￡ ü ?E ^μ?>×f (x;y) ^E ￥ ??f ?5f (E) ^> uW. 5