1. (10 marks) Determine whether each statement is true or false, justifying your answer. (a) (2 marks) The vector field F(x, y) = (2r + 3y, -3x - 2y) is conservative on IR. (b) (2 marks) If f : 12 - R is O' then [. Vf - dr = 0, where C is the unit circle. (c) (2 marks) The are length of the parametric curve r(() = (-2 + 4 cos(t), 3 + 4sin(t)). 1 E [0, T] is ST. (d) (2 marks) The curve xy - 6: + 7y - 1 =0 is a hyperbola. (e) (2 marks) The direction of steepest ascent of f (r, y) = r ty at the point (a, b) = (-1, 1) is u = (-- 1