evaluate (a) lim x→ x^2 - 36/x^2 + 5x - 6 (b) the demand curve of a firm is p= -10q + 5900 and its average cost is  A(q) = 2q^2 - 4q + 140 + 845/q. where q is the firm's output produced and sold. 1. derive an expression for the total revenue of the firm. 2. derive an expression for the firm's total profit function 3. derive an expression for the rate of change of profit function of the firm. 4. is the rate of change of profit increasing or decreasing when the firm's output level is q= 50? 5. determine the level of output for which the total profit of the firm is maximized  6. what is the firm's maximum profit

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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.