Math 234 Spring 2013 Exam 1 Version 1Monday, February 11, 2013Name: UIN:Circle the section you are registered for:ADA (9:00) ADD (12:00) ADG (3:00) CDC (11:00) CDF (2:00)ADB (10:00) ADE (1:00) CDA (8:00) CDD (12:00) CDG (3:00)ADC (11:00) ADF (2:00) CDB (9:00) CDE (1:00) CDH (11:00)1) You should have already checked into the exam and had your calculator approved. Noexam will be accepted from a student who does not check in before they start the exam.2) No baseball caps, hoodies, etc. or dark sunglasses. All hats are to be removed.3) All book bags should be closed and placed at the front of the classroom. Do not reachinto your bag for anything during the exam. If you need extra pencils, pull them out NOW.4) No cells phones. Turn them off now. If you are seen with a cell phone in hand during theexam it will be considered cheating and you will be asked to leave. This includes using it asa time-piece.5) No iPods or MP3s players, etc. Same rules as with cell phones.6) If you have a question, raise your hand and a proctor will come to you. If you have to usethe bathroom, do so NOW. You will not be permitted to leave the room and return duringthe exam.7) Every exam is worth a total of 100 points. Check to see that you have all of the pages.Including this cover sheet, each exam has 7 sides. Each problem is worth 16 points. Youwill receive 4 points for your name and section.8) Be sure to print your proper name clearly at the top of this page. Also circle the sectionfor which you are registered.9) If you finish early, quietly and respectfully get up and hand in your exam. You will needto show a picture ID when you hand in your exam.10) When time is up, you will be instructed to put down your writing utensil, close yourexam and remain seated. Anyone seen continuing to write after time is called will have theirexam marked and lose all points on the page they are writing on. Pull your IDs out NOWso that you have them ready.11) To ensure that you receive full credit, show all of your work.12) Good luck. You have 60 minutes to complete this exam.1(1) Find(a) limx→4(x2− 3x − 4)/(x2− 16)(b) limx→1x3− 5x2+ 4(c) limx→+∞(x2− 3x + 2)/(4 − 3x2)2(2) Suppose that the function f(x) is defined byf(x) =(1 − 5x if x < 1Ax2+ 2x − 3 if x ≥ 1.Find(a) limx→1−f(x)(b) limx→1+f(x)(c) the value of A such that f(x) is continuous at x = 13(3) Find all points on the graph off(x) =x + 1x2+ x + 1where the tangent line is horizontal.4(4) (a) State the definition of f0(x).(b) Use the the definition in (a) to compute f0(1) when f(x) =1√x.5(5) It is estimated that t years from now, the population of a certain suburban communitywill beP (t) = 20 −12t + 1thousand people.(a) What will the population of the community be 3 years from now?(b) By how much will the population increase during the third year?(c) What happens to P (t) as t gets larger and larger? Interpret your result.6(6) A bookstore can obtain a certain book from the publisher at a cost of $3 per copy.The bookstore has been offering the book at the price of $15 per copy, and at thisprice, has been selling 200 copies a month. The bookstore is planning to lower itsprice to stimulate sales and estimates that for each $1 reduction in the price, 20 morebooks will be sold each month. Express the bookstore’s monthly profit from the saleof this book as a function of the selling
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