MATH 3251, Midterm 2, Fall 1996
October 31, 1996.
50 points are divided between 4 problems (one page).
No books, no notes. Calculators are permitted.
1(a) (7 points). Given a point 
on
the plane curve 
, find symmetric equations for the tangent line
to the curve at point P.
(b) (3 points). Find the constant 
and 
for which the tangent line
to the curve at point P is given by the equation 
.
2(a) (7 points). Find the length of the curve
(b) (5 points). Find the curvature of 
for
arbitrary t.
3(a) (10 points). Find the length of the curve defined as the intersection of two surfaces
(b) (2 points). Find the curvature of the curve at the point with coordinates (1,2,3).
4(a) (6 points). For any constant 
,
find the curvature 
of the curve
at the point 
.
(b) (6 points). Find the minimal value of
as a function of b.
(c) (4 points). Find the maximal value of .
Some useful formulas: 
,
