1. [10] Calculate the limits: a) lim 5x- +7x-9 I-+00 -6.x7 +2 6) lim- - Inx (by applying the L'Hospital's rule) 2. [15] Use the price-demand equation x = f(p) =5(p-60) to find the values of p for which demand is elastic and the values for which demand is inelastic. 3. [15] Past sales records for a swimming-pool manufacturer indicate that the total number of swimming pools N (in thousands) sold during a year is given by: N(1) = 21 +13/2 where t is the number of months since the beginning of the year. Find N(9) and N'(9) and interpret these quantities. 4. [15] Find the first derivative of the following functions: a) Y=- x' -3 b ) f(x) =2In(x3 -3x +4) 5.[15] For the function f(x) =-+ x find the critical values, the intervals on which f(x) is X increasing, decreasing and local extrema