This is a calculus related question. Please answer the question as detail as will.

(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 -1x-+0x2(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 bydy = x(x2 + 1)2dxand the curve cuts the y-axis at the point (0, 1). Find the equation of this curve.(4 marks)