MAT-2130 Midterm: MATH 2130 App State Fall2013 Test2
Document Summary
Notice that the level curves of f (x, y) = x2 y2 are x2 y2 = c which are hyperbolas for c 6= 0 and y = x when c = 0. Also, remember that gradient vectors should be perpendicular to level curves and should point to higher ground : (10 points) let z = f (u, v) where u = x + y and v = x y. This is a level surface where f (x, y, z) = x2y + sin(xyz) + xz and f (x, y, z) = 2. Notice that f ( 1, 0, 2) = ( 1)20 + We know that f ( 1, 0, 2) will give us our normal vector. F ( 1, 0, 2) = h2( 1)0 + cos( 1(0)2) 0(2) + 2, ( 1)2 + cos( 1(0)2) ( 1)2, cos( 1(0)2) ( 1)0 + ( 1)i. = h0 + 0 + 2, 1 2, 0 1i = h2, 1, 1i.
