Please provide detail steps. R=9 in part (b).

(a) If A is a 2x2 matrix such that tr (A) =3 and tr( A? ) =5, find det (A). (4 marks) (b) If B and C are 5x5 matrices such that det (B) =-2 and det (C) = R+3, find det 2(BCT )"). (4 marks) (c) Evaluate lim - sin x -1 X-+0 x2 (4 marks) (d) If g(x) = e , where f (x) = x' +6x+9, compute g'(2). (4 marks) (e) The slope at any point (x, y ) on a curve is given by dy = x (x 2 + 1) 2 dx and the curve cuts the y-axis at the point (0, 1). Find the equation of this curve. (4 marks)