Question 1 Evaluate the following integrals. i) R ( x 5+ 3+x 3 ln2 x x4 )dx [2] ii) R x 2 1 + 0.2x dx [2] Question 2 The inventory for an item in a warehouse is given by I(t) = 120t cos(0.05(t 2 + 25)), where t is measured in days since the beginning of 2020. Find the average inventory done in the first ten days of the year. [3] Question 3 The marginal cost and the demand functions to produce q items by a company are respectively given by C 0 (q) = 6q2 + 390.06q and p = 2100 + 0.03q, where p is in rands. i) Find the total variable cost needed to produce 10 items. [1] ii) Find q that maximizes the profit of the company. [2]