Question 2 (TOTAL: 25 marks) (a) Evaluate lim So In(y+1)dy X+00 (5 marks) (b) Suppose the revenue function R(P) = ; where P is the price of the product. Use the definition of the derivative to find out R'(P). (5 marks) (c) Find out the first derivative of y2e2x = 3y + x2 evaluated at (0, 3). (5 marks) (d) Find out the equation of the tangent line to ye2x = 3y + x2 at (0, 3). (5 marks) (e) Suppose y is defined implicitly as a function of x by the following equation: g(xy + x) = x3e2y + In (x4), where g is a given differentiable function. Find an expression for y' or dy