An answer with no work receives no credit. You may use the back of a page if you need more space for a problem. Calculus iii (mac2313-13: circle true or false. Page 2 of 6 (a) (2 points) true. False u (v w) = (w v) u for all u, v, and w in r3. (b) (2 points) true of f exist at a. If f is di erentiable at a, then all rst-order, partial derivatives (c) (2 points) true. All surfaces are orientable. (d) (2 points) true identically zero. The divergence of the gradient of any smooth scalar eld is (e) (2 points) true. If ~f is a smooth vector eld, then ~ ( ~ ~f ) is a vector eld. (f) (2 points) true. The curl of the gradient of any smooth scalar eld is identically zero: (10 points) find the distance between the parallel planes 6z = 4y 2x and 9z = 1 3x + 6y.
