? E tc?f ?i? ? x1??????ZZZ???￥￥￥ f f f??? 1. !f ?F(x;y) ?@ (1) u×D : x0 ?a ? x ? x0 +ay0 ?b ? y ? y0 +b  ?? (2) F(x0;y0) = 0 (3)?x%? Hf ?F(x;y) ^y￥?ì??f ? 5 V¤? I 12 ?$ k￡ ü-. 2Z?x2 + y + sin(xy) = 0e??í ??¨? ?y = f(x)￥Z?V U$? ??¨? ?x = g(y)￥Z?V U$ 3Z?F(x;y) = y2 ?x2(1?x2) = 0 't?￥?í V·B1 ??? ′a ??a Oμ ??? ?￥f ?y = f(x). 4￡ üμ·B V?￥f ?y = y(x) ?@Z?sin+sinhy = xi p ? ?y0(x) ?sinhy = ey?e?y2 . 5Z?xy + zlny + exz = 1?P0(0;1;1)￥  #× = ?? ?? B ?M  ^ 6? ?M ￥f ?. 6 !f ^Bíf ? kùf? ?@ I 1HqZ? 2f(xy) = f(x)+f(y) ?(1,1)￥ #× = ? ??·B￥y1x￥f ?. 7 !μZ?x = y + ’(y) ?’(0) = 0 O??a < y < a Hj’0(y)j ? k < 1.￡ üi– > 0??– < x < – Hi·B￥ V±f ?y = y(x) ?@Z?x = y +’(y) Oy(0) = 0. 1 x2ZZZ???FFF￥￥￥ f f f??? 1 k) ?Z?F8 < : x2 +y2 = 12z2; x+y +z = 2 ?P0(1;?1;2)￥?í ?? ??? ?x = f(z)y = g(z)￥?f ?F. 2 p/ f ?F￥Qf ?F￥ ê? ? (1) !u = xcos yx;v = xsin yx p@x@u; @x@v; @y@u; @y@v (2) !u = ex +xsiny;v = ex ?xcosy p@x@u; @x@v; @y@u; @y@v. 3 !u = xr2v = yr2w = zr2 ?r = px2 +y2 +z2. (1) k p[u;v;w11M ￥Qf ?F (2)9 ?@(u;v;w)@(x;y;z). 4 !fi;’i ?? V± OFi(x1;￠￠￠xn) = fi(’1(x1);’2(x2);￠￠￠’n(xn))(i = 1;2;...n). p@(F1;F2;￠￠￠Fn)@(x 1;x2;￠￠￠xn) . 5 ? a ü?(0,1)?í ^?i ?? V±f ?f(x;y)?g(x;y) ? @f(0;1) = 1;g(0;1) = ?1 O [f(x;y)]3 +xg(x;y)?y = 0; [g(x;y)]3 +yf(x;y)?x = 0: 6 !8 >>> < >>>: u = f(x;y;z;t); g(y;z;t) = 0; h(z;t) = 0:  I 1Hq/u ^x;y￥f ?$ p@u@x; @u@y. 2 7 !f ?u = u(x)?Z?F 8> >>< >>>: u = f(x;y;z); g(x;y;z) = 0; h(x;y;z) = 0 ? ?? pdudx; d2udx2. 8 !z = z(x;y) ?@Z?F 8< : f(x;y;z;t) = 0; g(x;y;z;t) = 0: pdz. 9 !8 < : u = f(x?ut;y ?ut;z ?ut); g(x;y;z) = 0: p@u@x; @u@y.? Ht ^1M ? ^yM $ 10 !(x0;y0;z0;u0) ?@Z?F 8 >>> < >>> : f(x)+f(y)+f(z) = F(u); g(x;)+g(y)+g(z) = G(u); h(x;)+h(y)+h(z) = H(u): ? ú ?μ￥f ?L?μ ??￥? ?. (1) aB? ???￥ #× = ??x;y;zT1u￥f ?￥ sHq (2)f(x) = x;g(x) = x2;h(x) = x3￥ f?/  ?HqM?? I 1$ 11 !x = u;y = u1+uv;z = u1+uw |u;v1?￥1M w1?￥yM MDZ? x2@z@x +y2@z@y = z2: 3