Math 234 Spring 2014 Exam 1 Version 1Monday, February 17, 2014Name: UIN:Circle the section you are registered for:ADA (9:00 – Neriman) BDA (9:00 – Dileep) CDA (8:00 – Nima)ADB (10:00 – Neriman) BDB (10:00 – Dileep) CDB (9:00 – Nima)ADC (11:00 – Itziar) BDC (11:00 – Jiashun) CDC (11:00 – Michael)ADD (12:00 – Itziar) BDD (12:00 – Sean) CDD (12:00 – Michael)ADE (1:00 – Malik) BDE (1:00 – Argen) CDE (1:00 – Jaehoon)ADF (2:00 – Malik) BDF (2:00 – Argen) CDF (2:00 – Claire)ADG (3:00 – Alessandro) BDG (3:00 – Albert) CDG (3:00 – Claire)ADH (4:00 – Alessandro) BDH (4:00 – Albert) CDH (11:00 – Sean)(1) You should have already checked into the exam and had your calculator approved.No exam will be accepted from a student who does not check in before they start theexam.(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 notreach into your bag for anything during the exam. If you need extra pencils, pullthem out NOW.(4) No cells phones. Turn them off now. If you are seen with a cell phone in hand duringthe exam it will be considered cheating and you will be asked to leave. This includesusing it as a 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 haveto use the bathroom, do so NOW. You will not be permitted to leave the room andreturn during the exam.(7) Every exam is worth a total of 100 points. Check to see that you have all of thepages. Including this cover sheet, each exam has 7 sides. Each problem is worth 16points. You will 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 thesection for which you are registered.(9) If you finish early, quietly and respectfully get up and 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 willhave their exam marked and lose all points on the page they are writing on.(11) To ensure that you receive full credit, show all of your work.(12) Good luck. You have 60 minutes to complete this exam.Problem Problem Problem Problem Problem Problem Problem Problem Total1 2 3 4 5 6 7 8 Points1(1) Compute the following limits or state that they do not exist.(a) limx→−2x2+ x − 2x2− x − 6(b) limx→∞3x3− 4x2+ 2(2x + 1)32(2) Charlotte’s Sweet Shoppe specializes in producing boxes of chocolate covered toffee.Each box costs $4 to produce and can be sold for $10. Assume that Charlotte’s hasfixed daily overhead costs of $150.(a) Write a function for Charlotte’s total daily cost if she produces x boxes of choco-late covered toffee.(b) Assuming that Charlotte sells every box of chocolate covered toffees that sheproduces, what is the daily revenue function?(c) How many boxes of toffee will she need to sell each day in order to break even?3(3) (a) Which of the following is the correct definition of the derivative of f (x)?(i) f0(x) = limh→0f(x + h) + f(x)h(ii) f0(x) = limh→0f(x + h) − f(x)h(iii) f0(x) =f(x + h) − f(x)h(iv) f0(x) = limx→0f(x + h) − f(x)x(b) Use the definition of the derivative to compute f0(x) wheref(x) = x2+ 3x4(4) A concert promoter is trying to decide what price to charge per ticket. She finds thatshe can sell 1000 tickets at $50 each. For every $1 increase in ticket price, she willsell 10 fewer tickets.Let x be the number of $1 price increases.(a) Express p, the price of each ticket, as a function of x.(b) Find an expression for n, the number of tickets sold, after x price increases(c) Find an expression for the total revenue after x price increases.(d) What value of x maximizes revenue?(e) What price should she charge for each ticket to maximize revenue? How manytickets will she sell at that price?(f) What will her maximum revenue be?5(5) Find all values k so that f (x) is continuous for all real values of x.f(x) =(x2+ 2x if x ≤ 2x3+ kx2+ 4 if x > 26(6) How long will it take $1 to triple at an annual inflation rate of 8% compoundedcontinuously?7(7) Find the domain of the following functions:(a) y =√x − 22x + 3(b) y = ln(x + 7)8(8) Evaluate the following:(a) log3(81)(b) (13)−3(c) log4(8)(d)
View Full Document
Unlocking...