Hello, could someone please correct this exercise?( Especially from question 3 onwards if it takes you too long, the previous questions I will be able to manage I think.)

Exercise 7: 1. Provide the domain of definition and calculate the derivative of the following functions: . m(x) = In(x2 + 2x) . r(x) = 2. Let g be the function defined on ]0, too[ by g(x) = In(x + 1) - In(x). a) Show that for all x > 0, g(x) = In (1 + 2). b) Examine the sign of g(x). c) Determine the limits of g at 0 and too. 3. Let f be the function defined on ]0, too by f (x) = x +.2 + In(x + 1) - In(x), and Of its graph in a Cartesian coordinate system (0, i, j). (0, i , ;) i and j are Utilizing the results from part 1, justify the following statements: vectors a) The y-axis is an asymptote to the graph Cf. b) The line D with equation y = x + 2 is an asymptote to Of as a approaches +OO. c) The graph Cf lies above the line D