I need help with the questions in the picture. Please let me know if there is any question

4. Consider functions of the form ymeds. (a) Show that edx =1(-e*). (3 marks] (b) Let k = 0.5 (i) Sketch the graph of y=ess, for -Isx53, indicating the coordinates of the j-intercept. (ii) Shade the region enclosed by this graph, the x-axis , j-axis and the line x=1 . (iii) Find the area of this region. (5 marks] 5.) The diagram below shows the shaded region R enclosed by the graph of y =2xv1+x , the x-axis, and the vertical line x = k. y =2xvl+x I (a) Find dr [3 marks] (b) Using the substitution w = 1+ x' or otherwise, show that [2xvitx' dr = 2(1+x])+c. [3 marks] (c) Given that the area of R equals 1, find the value of k. [3 marks]