I need help with these three problems on knowing how to do them step by step and it is helpful if it is handwritten. And what theorems to use.

1. Newton Automobiles is a new company in Roanoke, VA. The sales team at Newton Automobilies estimate that the total amount of money, in millions, that Newton Autombiles will make from selling cars after t years is given by the revenue equation R(t) = 6t + In(t + 1), t 2 0. The total cost, in millions, of running the manufacturing plant for t years is given by C(t) = 2tsin?(It) +5, t20. A company begins to make a profit when its revenue exceeds its cost. The point at which the revenue equals the cost the first two years. is known as the Break Even Point. Use a theorem from class to show that the company is expected to break even in (That is, show that the two graphs of R(t) and C(t) intersect at some point in the interval [0, 2].) (5 points) 2. Consider the function x- 2 -5 -75 x - 5 Using the definition of continuity, find the values of the constants a and b that make f continuous on (-7, co). Justify why your choice of a, b make the function continuous at all x-values. (10 points) 4. Find all the horizontal asymptotes for the following function: (10 points) 3.x - 1 x 2 2 4 2