1. Let c be a positive number, and let A > 0 represent the initial value of a population. a) Show that the function p(t) = (A^(-c) - ct)^(-1/c) satisfies the differential equation p'(t) = (p(t))^(1+c) b) What happens to p(t) as t > (A^(-c)/c) from the left? 2. Find the Maclaurin series for the functions sinh(x) and cosh(x) by using the Maclaurin series for ex and the defnitions of sinh(x) and cosh(x) in terms of ex. Compute the radius of convergence for each series.