11
: .
1.
2.
1. . z, x = x(u) 0, z = z(u), u I, , z.
1) x, y, z, (, , z): u ′ , Oz, v - ′′ .
2) ?
3) u = const () v = const () ?
. 1) = (u) cos v, y = (u) sin v, z = z(u), (u;v) I [0; ).
2) .
3) , ( ).
2. x = sin u, y = 0, z = lntg + cos u, u (0; ), z ().
1) x, y, z, u v, 1.
2) u = const v = const?
3) ; .
. 1) = sin u cosv, y = sin u sinv, z = lntg + cos u, (u;v) (0; ) [0; ).
2) () , ().
3. . , = (u), u I, , l () (), .. .
1) , : u ′ , , , v ( = v , v R).
2) u = const v = const ?
. 1) = (u) + v , u I, v R.
2) u = u0 , u0, v = v0 , │v0│().
4. , , z, 2 + 2 = 1, z = 0,
= (1; 1; 1).
. (x z)2 + (y z)2 1 = 0.
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. , , , .
= (u) + v ,
= (u), u I, , , , v R.
5. , , z, (1; 1; 1), , 2 + 2 = 1, z = 0.
. (x z)2 + (y z)2 (z 1)2 = 0.
. , , , ( ).
= + v ,
- ( ), = , u I, ( ) u, v R.