3. Show that the power series (a)-(c) have the same radius of convergence. Then show that (a) diverges at both endpoints, (b) converges at one endpoint but diverges at the other, and (c) converges at both endpoints. x" п3 x" (c) n23n (a) x" (b) n=1 n=1 n=1

1. The quantity, Q, in tons of material at a municipal waste site is a function of the number of years since 2000 with Q = f(t) = 6t* + 200 Find f (20), f'(20), and the relative rate of change at t = 20. Interpret your answers in terms of waste.

Find the radius of convergence and interval of convergence of the series. I need help with this problem.

le) (b) 2E" 2" 12. Check the convergence of the following power series, find the radius and interval of conver- gence: ( a) Σ" (x+ n)" ( b) Σ Also find the sum as a function of x for this problem. 13. Find the Taylor series generated by ƒ at r = a and the Maclaurin series: (a) f(x) = 1/x², a = 1 (b) f(x) = xª + x² + 1, a = -2 14. Find the Taylor polynomials of order 1,2,3 for the function f at a: (a) f(x)= /T, a = 4 (b) f(r) = cos r, a = r /4 15. (a) Calculate e with an error of less than 10-º. (b) Estimate the error in the approximation sinh(x) = x + (r"/3!) when |r| < 0.5. (c) How close is the approximation sin(x) = r when |æ| < 10¬³? For which of these values of r is a< sin(x)? %3D