問題1：Show that the parametrized surface
X(u,v)=(v*cosu,v*sinu,a*u), a≠0,
is regular. Compute its normal vector N(u,v) and show that along
the coordinate line u=u0 the tangent plane of X rotates about this
line in such a way that the tangent of its angle with the z axis is
proportional to the distance v(=√(x^2+y^2)) of the point X(u0,v) to
the z axis.
這一題的前面兩個問題(證明regular以及計算normal vector)沒有問題，但是最後面
的問題看不懂它要證明什麼
問題2：(Theory of Contact.) Two regular surface, S and S', in R^3,
which have a point p in common, are said to have contact of order≧1 at p
if there exist parametrizations with the same domain X(u,v), X'(u,v)
at p of S and S', respectively, such that Xu=X'u and Xv=X'v at p(兩個參數式
在p點分別對u,v偏微會相等). If, moreover, some of the second partial
derivatives are different at p, the contact is said to be of order
exactly equal to 1. Prove that
e) If two surfaces have contact of order≧1 at p, then (d/r)=0,r→0,
where d is the length of the segment which is determined by the intersections
with the surfaces of some parallel to the common normal, at a distance r
from this normal.
題目一開始先定義兩個regular surface的contact定義，但不懂問題e的意思
請各位大大幫小弟解惑一下，感謝
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