Please help me out with these questions. I tried to study but still hitting dead end. Thank you very much.

6. Consider a particle travelling along the elliptical path c() = = cost , 2 sin t ). If the particle is released at time t = -", find the position of the particle at time t = = + 5. 7. Use the method of power series to solve the differential equation y' = =y, where & a constant. 8. Find the Taylor series of f (x) = log (3 - x) about x = 2. Is it appropriate to approximate f(0) with a Taylor polynomial about x = 2? 9. Find a function f (x) with power series / (x) = >n n3x". 10. Use a power series to show that 0.999... = 1