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3. Let P(p) = 40p - 2p' + 50 be the weekly profit, in thousands of dollars, resulting from selling a good at a price of $p. (a) What value of p maximizes profit? (b) What is the maximum possible profit? 4. For a particular city in the southern hemisphere, the daily average temperature varies throughout the year. The maximum average temperature of 82" F occurs every year on February 1, and the minimum of 38" F occurs every year on August 1 . (a) Find a possible formula for 7(t), the daily average temperature { months after January 1. (b) Find two values of t in the interval [1, 13] such that T(t) = 70" F. 5. Solve the equation 5eat? = 20 for . 6. If tan 0 = -3 and cose > 0, find csce. 7. The graph of f is shown below. List all values of a for which lim f(x) does NOT exist.1 -3 -2 -1 4 . -1