1. Consider the function f(x) = 4x6 25102. (a) Determine algebraically if f (x) is even or odd. (b) Based on your answer to part (a), use a symmetry property of denite integrals to simplify 1 f f (as) das and then solve the resulting integral. 1 1 (c) Compute the value of f f (9:) dx without using any symmetry properties. 1 (d) Is the calculation in part (b) or (c) easier to do? 2. The rate of increase of the number of married couples M (in thousands) in the United States from 1970 to 2005 can be modeled by M dd_t = 1.218732 44.721: + 709.1 Where t is the time in years, with t = 0 corresponding to 1970. The number of married couples in 2005 was 59,513 thousand. (Data from the US Census Bureau) (a) Find the model for the number of married couples in the US. (b) Use the model to predict the number of married couples in the US in 2012 (round to the nearest Whole number). (c) According to this model, would you expect the number of couples in the US to continue to increase? Give a clear and complete justication for your decision