8. (a) Find the area enclosed by one loop of the curve r = 4sin 30. [Hint: Consider only the interval 0 5 05 , (b) Write an expression for the arc length of the loop but do not evaluate it. 9. (a) Find the first five terms of the Taylor series for f(x) = sin x about 4 (b) What is the radius of convergence of the series obtained in part (a)? (Justify your answer by using a suitable convergence test. ) (c) Prove that the series converges to, that is, represents the function f(x) = sinc