please help to answer all the questions with clear steps.

7 The variables x and y satisfy the differential equation dy dx - = xetty and it is given that y = 0 when x = 0. (i) Solve the differential equation and obtain an expression for y in terms of x. [7] (ii) Explain briefly why x can only take values less than I. [1] 8 The line / has equation r = ( 2 ) + 2 () The plane p has equation r. ( -1 ) = 6. (i) Show that / is parallel to p. [3] (ii) A line m lies in the plane p and is perpendicular to /. The line m passes through the point with coordinates (5, 3, 1). Find a vector equation for m. [6] 9 Let f(x ) = 3x + 6x - 8 x(x2+ 2) (i) Express f(x) in the form A + 5 , Cx + D $ 72 +2 [5] (ii) Show that [ f(x) dr = 3 - In 4. [5] 10 (a) Find the complex number z satisfying the equation z' + 1 = 2iz, where z* denotes the complex conjugate of z. Give your answer in the form x + iy, where x and y are real. [5] (b) (i) On a sketch of an Argand diagram, shade the region whose points represent complex numbers satisfying the inequalities (z + 1 - 3i| 3. where Im z denotes the imaginary part of z. (4] (ii) Determine the difference between the greatest and least values of arg z for points lying in this region. [2]