BC Module 7 DBA (written portion) This is a NON-CALCULATOR assignment. Show all your work to support your answers. (5 points each)

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

(a) Find lim x 0 [(f( x)+2) / (sinx)]. Show the work that leads to your answer.

(b) Write an equation for the line tangent to the graph of f at the point (0, 2). Use the tangent line to approximate f(0.3).

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

(d) Find y = f(x), the particular solution to the differential equation that passes through (0, 2).