Limits To determine what they should charge for their service they use data from a few test sales and also reasonable expectations for what people are willing to pay for the service. They find that the price (in thousands) that should be set is described by the value of this limit: [6] lim Vt+8-3 t-1 where t represent the number of months the company has been operating ta a) Determine the price of the service after 8 months? Use proper limit notations. b) Determine the price of the service after 1 month? Use proper limit notations.Derivatives of functions The revenue of the company in millions is modelled by the function f() = (2+ 3)3 where t is the number of months it has been operating. [6] a) How fast is revenue changing after 3 months? b) Is the function above differentiable everywhere? Explain using derivatives.Optimization The profit model is given by the function: f(x) = cos(x) (3") where x represents the number of new customers each year in hundreds. Determine how many new customers are needed to maximize profit if the company cannot support more than 800 new customers each year. [6]