Consider the differential equation dy/dx=y^2(2x+2). Let y=f(x) be the particular solution to the differential equation with initial condition f(0)=-1.

a) Find the limit of (f(x)+1)/sin(x) as x approaches to 0. Show the work that leads to your answer.

b) Use Euler's method, starting at x=0 with two steps of equal size, to approximate f(1/2).

c) Find y=f(x), the particular solution to the differential equation with initial condition f(0)=-1.

Please show all your work.

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