8. Suppose that the net earnings of a company at time t are being generated at the rate of 25 + 5t million dollars per year, and the general formula for present value of a continuous stream of income is: PV =| K(t)e¬rt dt K(t) is the amount per year of the annual rate of income at time t; r is the annual interest rate of invested money; and T, to T, (years) is the time period of the income stream. (a)Write a definite integral that gives the present value of the company's earnings over the next 2 years using 10% interest rate. (b) Compute the present value from part (a). (c) If a potential buyer of this company offers 50 million dollars to buy the company outright, determine if the owner of the company should sell now, or should keep the company for two years. Explain your reasoning.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.