Math 234 Spring 2016 Exam 1 Version 1Wednesday, February 17th, 2015Name: UIN:Circle the section you are registered for:ADA (Vanessa 9AM) ADB (Vanessa 10AM) ADC (Chris 11AM) ADD (Chris 12PM)ADE (Mingyu 1PM) ADF (Mingyu 2PM) ADG (Derek 3PM) ADH (Derek 4PM)BDA (Mary 9AM) BDB (Mary 10AM) BDC (Ian 11AM) BDD (Matthew 12PM)BDE (Matthew 1PM) BDF (Ian 2PM) BDG (Corrine 3PM) BDH (Corrine 4PM)CDA CDB (Shiyu 9AM) CDC (Shiyu 11AM) CDD (Panu 12PM)CDE (Panu 1PM) CDF (Neriman 2PM) CDG (Neriman 3PM) CDH (Joseph 11AM)(1) No baseball caps, hoodies, etc. or dark sunglasses. All hats are to be removed.(2) All bags, purses, jackets, and other personal items should be at the front of the room.(3) If you have a question, raise your hand and a proctor will come to you. If you haveto use the bathroom, do so NOW. You will not be permitted to leave the room andreturn during the exam.(4) No cells phones, i-Pods, MP3 players. Turn them off now. If you are seen these itemsin hand during the exam it will be considered cheating and you will be asked to leave.This includes using it as a time-piece.(5) Be sure to print your proper name clearly at the top of this page. Also circle thesection for which you are registered.(6) If you finish early, quietly and respectfully get up and hand in your exam.(7) 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 willhave their exam marked and lose all points on the page they are writing on.(8) To ensure that you receive full credit, show all of your work.(9) Good luck. You have 60 minutes to complete this exam.1(1) (Break Even Problem)Joanne is knitting artisinal winter hats for dogs for her store, Kitschy Stichy, inBrooklyn. It costs her $2 in materials to make an Anglican Argyle Hat, and $3 inmaterials to make a Scandinavian Ski Hat. Her fixed monthly overhead at the storeis $500. She sells Anglican Argyle Hats for $10 each, and Scandinavian Ski Hats for$15 each.(a) In the month of January, yarn for the Scandinavian Ski Hat was unavailable (dueto a shortage of organic Alpaca wool), and Joanne only made and sold AnglicanArgyle hats during January. Let x = the number of Anglican Argyle Hats. Writeequations for cost and revenue functions (C(x) and R(x)) for Joanne’s store inJanuary.(b) How many Anglican Argyle Hats for Dogs must Joanne sell in January to breakeven?(c) How many Anglican Argyle Hats for Dogs must Joanne sell in January to makea profit of $1000?2(2) Settlement ProblemA company must pay a $100,000 settlement in 5 years.(a) What amount must be deposited at 5% interest, compounded quarterly, to haveenough money for this settlement?(b) Suppose the company can only deposit $25,000 now. How much more will beneeded in 5 years?(c) The advertised interest rate in this account is 5%, but what is the effective in-terest rate? (i.e. annual yield?)(d) Now suppose the company can deposit $75,000 in an account that pays interestcontinuously. What interest rate would they need to accumulate the $100,000in 5 years?3(3) Matching graphs to derivativesI.-4 -2 2 4-4-224-4 -2 2 4-4-224-4 -2 2 4-10-5510-4 -2 2 4-10-5510-4 -2 2 4-10-5510-4 -2 2 4-10-5510-4 -2 2 4-10-5510-4 -2 2 4-10-55104(4) Consider the graph below when answering the following questions. For each part,write a number, +∞, −∞, or DNE (does not exist).-6 -4 -2 2 4 6-224limx→−3−f(x) = limx→−3+f(x) =limx→−3f(x) = f(−3) =limx→1−f(x) = limx→1+f(x) =limx→1f(x) = f(1) =limx→3−f(x) = limx→3+f(x) =limx→3f(x) = f(3) =limx→−∞f(x) = limx→+∞f(x) =5(5) Consider the graph of f(x) below. List all the points x = a where f (x) is not differ-entiable, and STATE YOUR REASON WHY FOR EACH POINT.- 4 - 2 2 4- 4- 3- 2- 11236(6) Using the definition of the derivative, determine f0(x) if(a) f (x) =1 − x2 + x(b) f (x) =2 + x1 − x7(7) Suppose that limx→2f(x) = A(a) If limx→2g(x) = 2, determine all values of A so thatlimx→2xg(x)f(x)pf(x) + g(x)= 1(b) If limx→2g(x) = 1, determine all values of A so thatlimx→2xg(x)f(x)pf(x) + g(x)= 18(8) Suppose that(a) limx→a(2f(x) − h(x)) = 1 and limx→a(f(x) + h(x)) = 2. Determine limx→af(x)h(x)(b) limx→a(f(x) − 2h(x)) = 2 and limx→a(f(x) + h(x)) = 1. Determine limx→af(x)h(x)(9) (BONUS)Determine(a)limx→∞√9x2+ x − 3x(b)limx→∞√4x2+ 2x −
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