(3) Define sinc x = sin x for x * 0 and sinc 0 = 1. (a Show that lim sinc x = 1. x-+0 (b) Show that lim sinc x = lim sinc x = 0. (c) Show that sinc x = 0 if and only if x is a nonzero integer multiple of . (d) Show that & sinc x = 0 if and only if sinc x = cos x. (e) Show that each point at which sinc x = cosa is in fact a local extremum.(1) We want to design a rectangular prism box with a square base that has a total volume of 1 m3 With the lowest total cost, Where the material used for the sides and bottom costs $10 per square meter and the material used for the lid costs $5 per square meter. (a) If the side length of the base is a and the height is h, determine a formula for the cost in terms of a and h. (b) Use the constraint on the volume to determine a formula for the cost in terms of a single parameter. (C) Determine the dimensions of the box that minimize the cost