11. at the halfway point through these questions, you probably need a break. what should i do? a) give a really hard problem that is so hard you won't even try it, thus giving you a break b) give a really long problem that will keep you from trying the next 9 problems too soon, thus giving you a break c) tell you the next 5 questions are based on material you have still need to read about, thus giving you a break from these questions for a while d) give everyone 4 free points. 12. (t f) if the divergence of a vector field f(z. y,) is zero, then the curl must be the zero vector as well 13. (t f) the function f(x, y) = e-# + v5 is a potential function for the vector field f 0, then vf ,0 for any c > 0. 16. when simplified, the value of the derivative of f(r, y) = e-z* at the point (1,1) in the direction of the vector is in the form a/b, where a and b are integers. enter their sum a + b 17. (t f) suppose you know that vf(a, 6) = and that the directional derivative of f in the direction from the point (a, b) to the point (a+1,b+1) is positive. then the directional derivative of f in the direction from the point (a, b) to the point (a-1,b-1) must be negative. 18. suppose f(r, y) is known to be a conservative vector field. then all of the following statements except one must be true. which one is not definitely true? a)vx f bv f 0 c) if c goes from (1,0) to (-1,0) around the top half of the unit eircle, while c2 goes from (1,0) to (-1,0) around the bottom half of the unit circle, then f-dr= f di d) there is a scalar function f(z, y) such that f = vf.