微積分期中考每題十分共十題總分100分

1、<p>　　微積分期中考 每題十分 共十題 總分100分</p><p>　　日期:95.11.23</p><p>　　Find equations for these lines that is tangent to the graph of f for the given value of x.</p><p>　　(a)

2、 (b) </p><p>　　Find the give limit or show it does not exist . If the limit is infinite, indicate whether it is or -.</p><p>　　(a) (b) </p><p>　　(c) (d) </p&g

3、t;<p>　　List all the values of x for which the give function is not continuous </p><p>　　(a) (b)</p><p>　　Discuss the continuity of the function </p><p>　　Find th

4、e derivative of the given function </p><p>　　(a) (b)</p><p>　　(c) (d)</p><p>　　Find for given value of x </p><p>　　(a); for x=1&

5、lt;/p><p>　　(b), for x=3</p><p>　　A bookstore can obtain a certain gift book from the publisher at a cost of $3 per book. The bookstore has been offering the book at price of $15 per copy, and at

6、this price, has been selling 200 copies a month. The bookstore is planning to lower its price to stimulate sales and estimates that for each $1 reduction in the price, 20 more books will be sold each month. Express the b

7、ookstore’s monthly profit from the sales of this book as a function of the selling price, draw the graph, and estimate</p><p>　　A manufacturer can sell a certain product for $80 per unit. Total cost consists

8、 of a fixed overhead of $4,500 plus production costs of $50 per unit.</p><p>　　How many units must the manufacturer sell to break even?</p><p>　　What is the manufacturer’s profit or loss if 200

9、units are sold?</p><p>　　How many units must the manufacturer sell to realize a profit of $900?</p><p>　　An importer of Brazilian coffee estimates that local consumers will buy approximately D(p

10、)= pounds of the coffee per week when the price is p dollars per pound. It is also estimated that t weeks from now, the price of Brazilian coffee will be p(t)=6 dollars per pound.</p><p>　　At what rate will

11、the demand for coffee be changing with respect to price when the price is $9?</p><p>　　At what rate will the demand for coffee be changing with respect to time 10 weeks from now? Will the demand be increasin

12、g or decreasing at this time?</p><p>　　Bea Johnson, the owner of the Bea Nice boutique, estimates that when a particular kind of perfume is priced at p dollars per bottle, she will sell B(p)= </p>&l

13、t;p>　　bottles per month at a total cost of dollars</p><p>　　Express Bea’s profit P(p) as a function of the price p per bottle.</p><p>　　At what rate is the profit changing with respect to p