Midterm 1 solutions - page 1 of 3. February 21, 2007: (25 points) let g(x, y) = ex+y and r : r r2 be a function where r(0) = (cid:20) r (0) =(cid:20) 1. Find f (0) where f (t) = g(r(t)). We use the special case of the chain rule: F (0) = g(r(0)) r (0) = g(1, 1) (cid:20)1. Thus, plugging in x = 1, y = 1, ex+y = e0 = 1 and thus. Write your answer in the form ax + by + cz + d = 0. In order to nd the equation of the plane, we will select a point on it, say c1(0) = (2, 0, 1), nd a non-zero normal vector n, and write. However, in the present case we see right away that v2 = v1, which means that the lines are parallel. Thus, we do not get in this way a non-zero normal vector.
