A26.1 (i) (2 marks) Recall the function secht = 1/ cosht. Show that sech't + tanh t = 1 (te R). (ii) (4 marks) Let F : R - R3 be the space curve tanh t T(t) = sech t (t ER). [log cosh t Calculate I'(t) and show that I' has unit speed. (iii) (4 marks) Calculate I"(t); hence find the curvature of I. A26.2 Let 0 > -1. (i) (4 marks) Find f'(x) and f"(x). (ii) (6 marks) For 0 -1}. A26.4 (i) (4 marks) When u = ry and v = y/x, compute the Jacobian determinants a(u, v) o(x, y) a(x, y) O (u, v) (x, y > 0). (ii) (6 marks) Find the area of the region R in the positive quadrant that is bounded by the curves Ty =a, ry =b; y = (1/2)x, y = 2x, where 0