Any help with these problems (with work, no calculator!) would be appreciated! Particularly need some help with problems 2 and 4.

2) Consider the differential equation dy = 2xy Let y=f(x) be the dx particular solution to this differential equation with initial condition f (4) =2. Find lim x - f ( x ) ] x-4 sin (nx)\f7 ) What is the volume of the solid generated by revolving the area bounded by y = e*, x=0, and x =1 about the x-axis? a ) 7 (e-1) b ) 2 C ) 2 2 -1) d) m(e -1) e) None R ( x ) = e - 0 S ex dx ft 8) A balloon was being inflated at a rate of 28 but burst when min 13 its volume reached 3- ift'. At what rate was the radius expanding 81 when the balloon burst? Leave your answer in terms of