# C 2 pts the comedy club must pay the comedian 6 for

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(c) (2 pts) The comedy club must pay the comedian \$6 for every ticket sold. Find a formula for C ( p ), the cost per show when the ticket price is p dollars. (d) (2 pts) Find a formula for π ( p ), the profit per show when the ticket price is p dollars. (e) (3 pts) What ticket price maximizes the comedy club’s profits?

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8. At a price of p dollars per cellphone case, the supply per week of hand-made cellphone cases is q = 2 p - 10 and the demand per week is q = - 3 p + 90. (a) (4 pts) Find the equilibrium price and equilibrium quantity. (b) (4 pts) A tax of \$2 . 50 per cellphone case is imposed on suppliers. What is the new equilibrium price and equilibrium quantity? (c) (2 pts) How much revenue does the government generate from this tax each week?
9. Compute the limits or explain why they do not exist. (a) (4 pts) lim x 9 2 x - 6 x - 9 (b) (3 pts) lim x 4 1 x - 4 - 1 4 (c) (4 pts) lim x →- 2 x 2 - x - 6 x 2 - 4 (d) (3 pts) lim x →∞ 3 x 3 - 1 x 3 - 10 x 2

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10. (a) (4 pts) Let g ( x ) = ln ( 3+ x 5 - x ) . Find a formula for g - 1 ( x ). (b) (3 pts) Does there exist a value for x such that x 4 + 6 x + 1 = 0? Justify your answer (if you answer “Yes,” you do not need to find the value of x ).
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