04faex1 - Math 211 ‘ Fall 2004 Exam I ‘ S Bolotin Your...

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Unformatted text preview: Math 211 ‘ . Fall 2004 Exam I ‘ S. Bolotin Your Name: Your TA: Your Section Meeting time: PROBLEM POINTS SCORE - - - - - r - Show all your work: no work - no credit. Leave your answers in exact forms (using 6, ln 2, \/§ and similar numbers). Circle your answer. You may use the last page as scratch paper, but it will not be checked. Hand in your exam, together with the formula sheet, to your TA. .Math 211 - ExamI - Bolotin - 9/29/04 Page2 I. (20 points) In (a) and (b) find the limit, if it exists, or show that the limit does not exist. ) 1. x+1 (a wig-11 $2+6x+5 _ x2 — 21: + 1 $2—2$+1 ('c) Find vertical and horizontal asymptotes for the graph y = 6:1: + 2502 Math 211 — Exam1'4 Bolotin - 9/29/04 Page3 II. (20 points) (a) Find'f’(:c) for the function f(a:) = 2\/E+ ~5- ~ 3:13—1/3. a: (b) Find f”(:z:). Math 211 - ExamI - Bolotin - 9/29/04 Page4 III. (20 points) (3.) Using the definition of the derivative as a limit find f’(1) for 3 the function f(:c) = 2x 3. (b) Find an equation of the tangent line to the graph y 2 at the point 213—3 m=1,y=—3. Math 211 - ExamI - Bolotin - 9/29/04 Page5 IV. (20 points) (a) Suppose you plan to retire in 40 years, and would like to have a million dollars at your retirement. You can invest your money with interest 5% compounded continuously for these 40 years. How much money you should invest now? Leave your answer in an exact form. (b) Suppose the interest is compounded quarterly (4 times a year), with the interest rate 8%, and you invest half a million dollars now. In how many years you will have a million? Leave your answer in an exact form. Math 211 - ExamI - Bolotin - 9/29/04 Page6 V. (20 points) The cost of producing one car is 10 thousand dollars. Research shows that if the selling price is raised by one thousand, then 10 fewer cars per week will be sold. If the selling price is set at 15 thousands, a hundred cars per week are sold. v (a) Find the number q of cars sold per week as a function of the selling price p. (b) Find the weekly revenue R(p) as a function of the selling price. (c) Find the weekly profit P(p) as a function of the selling price. (d) Find P' (p) and determine up to what level it makes sense to increase the price. Math 211 - ExamI - Bolotin - 9/29/04 Page7 Scrafcch paper ...
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