View Single Post
helpmeimdumb is offline
Feb27-12, 10:51 PM
P: 3
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


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


f(0.3)≈2/3 (0.3)+2ln3≈2.39722≈2.397


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

Here is where I run into problems. Can anybody help me with the rest? Any help would be greatly appreciated.
Phys.Org News Partner Science news on
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes