CSCE 4230  Homework #7


     Due date:  Thursday, Apr 23



     1)  Specify three representations of the line defined by points
         p1 = (x1,y1) and p2 = (x2,y2).

         a)  Functional form:  y = f(x).  (Assume x2-x1 is nonzero.)

         b)  Implicit form:  f(x,y) = 0.

         c)  Parametric form:  p(t) = (x(t),y(t)).  (Specify the range
             of parameter values.)


                                        2
     2)  Let f(x) = A + B sin(x) + C sin (x).  Find A, B, and C such
         that f(0) = 3, f'(0) = 2, and f(pi/2) = 1.


     3)  Let Q(t) be a quadratic polynomial such that Q(0) = 0,
         Q(1) = 2, and Q(3) = 6.  Use Lagrangian interpolation to
         obtain Q(2).


     4)  Let p0, p1, and p2 be points in the plane.

         a)  Specify a parametric representation of a planar curve C(t)
             that satisfies C(t0) = p0, C(t1) = p1, and C(t2) = p2.
             The components of C should be quadratic polynomials in t.

         b)  Specify the formula for C(t) with t0 = 0, t1 = 1, and
             t2 = 2.

         c)  Specify the derivative C'(t) with t0 = 0, t1 = 1, and
             t2 = 2.