Question

True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented clockwise and C2 is the sme square but traversed twice in the opposite direction If F . dr = 3, then F . dr--6匝 C2 (4) If Ci and Ca are oriented curves, and the length of Ci is greater than the length of (5) A parametrization of the graph of y -Inr for >0 is given by r-e,y-t for (6) Both double and triple integrals can be used to compute volumeT F (7 If gradf-3,-2)-(1,-1),then fincreases as we move in the i direction at (-3,-2) (8) The function f(r,y)- sin(1 +e)must have a global minimum in the square region D (9) The plane :-2x + 3y has normal vector 2i + 3j. (10) If the contours for f(ry)get claser toget her in a certain direction, then fis increasing in that direction. TF

Answer 1

.tr 9 η jnatt, n ny be L-er than 2c78 be Lers than 12) scude. 3)(o) (이-), 0p) oppoiile.dneth, ce mて 2