1. The problem statement, all variables and given/known data 1. The slope of a function at any point (x,y) is 〖2e〗^x/(e^x+2) . The point (0,2ln3) is on the graph of f. (A) Write an equation of the tangent line to the graph of f at x=0. (B) Use the tangent line in part A to approximate f(0.3) to the nearest thousandth. (C) Solve the differential equation dy/(dx )=(2e^x)/(e^x+2) with the initial condition f(0)=2ln3. (D) Use the solution in part C to find f(0.3) to the nearest thousandth. 2. Relevant equations 3. The attempt at a solution (A) dy/(dx )=(2e^x)/(e^x+2) At x=0, dy/dx=(2e^0)/(e^0+2)=2/3 Equation of tangent line at x=0: y-2ln3=2/3 (x-0) y-2ln3=2/3 x or y=2/3 x+2ln3 (B) f(0.3)≈2/3 (0.3)+2ln3≈2.39722≈2.397 (C) dy/dx=〖2e〗^x/(e^x+2) → dy=(2e^x)/(e^x+2) → ∫dy= ∫〖(2e^x)/(e^x+2) dx〗 Let u=e^x+2, du=e^x dx 2du=2e^x Here is where I run into problems. Can anybody help me with the rest? Any help would be greatly appreciated.