Calculus III

Please answer 3, 4, & 5

3. Sketch carefully the solution curves with initial points (0, 1), (0, 2), (0, 3), (0, 4), and (0, 5), without solving the equation (5 points): dP dt = (P - 3)2 4. Using Maclaurin series, compute the following (3 points): sin(x) - x lim x+0 x3 5. Find the interval of convergence (don't forget to check the endpoints!) of the following power series (5 points): (2x - 9)n Vn n= 1