1. Find the linear approximation of the following functions: a. f(x) = V2x + 81 at a = 0. b. f (x ) = x+= at a = 3. 2. Use the linear approximation to estimate the following quantity. Choose a value of a to produce a small error. a. In (0.96) f ( x) = a = L(x) = In (0.96) ~ L(0.96) = Percent error = b. V123 f ( x) = a =_ L(x ) = V123 ~ L(123) = Percent error = C. e 0.06 f ( x) = a =_ L(x) = 20.06 ~ L(0.06) = Percent error =Maximizing Problems 1. We would like to make a box with a square base. Suppose we only have 54m2 of material, nd the dimensions of the box that give the largest volume of the box. 2. You are ying for a vacation to I Iawaii. An airline has a policy on a checked in baggage: all baggage must be boxeshaped with sum of length, width and height not exceeding 64 in. What dimensions of a squarerbased box will allow you to check in the largest Volume under these conditions