MAT285-2005Spring

MAT285-2005Spring - Math 285 Final Exam, May 9, 2005 Name:...

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Unformatted text preview: Math 285 Final Exam, May 9, 2005 Name: SUID No.: CIRCLE your Instructors Name: Owour Salamy Wortman PLEASE READ: 1. Place all your work on these sheets. Do not add any sheets to this exam. 2. You may use a TI—83 on this exam. You may m use any other calculator nor may you use another student’s calculator. 3. Answers without supporting work/reasons will receive no credit. Label answers and give units when appropriate. 4. There are 10 problems (with parts) and 12 pages to this exam including this cover page and a blank page for scratch work. Be sure that you have all pages — check NOW! PLEASE put your name on each page in case your exam booklet comes apart. PLEASE DO NOT WRITE BELOW 10. Total NAME .......................................................... .. 1. (10 points) A bank offers an account that pays 2.75% interest per year, compounded continuously. A customer puts $50,000 in the account. (a). (4 points) How much will be in the customer’s account after 6 years? Give answer to the nearest cent. (b). (6 points) How long will it take for the customer’s account to double? Give answer to the nearest tenth of a year. 2. (6 points) At a local record shop, the number of CD’S sold on day a: of the year is given by: S(:1:)= 50 + 10sin(%ar +10). (a). (3 points) Find the period, amplitude, vertical shift (that is, midline) of (b). (3 points) Find the number of CD’S sold on day 180. Give answer to the nearest integer. NAME .......................................................... .. 3. (8 points) The graph of the function f(:c) is pictured below. 3.9; (a). (4 points) Using the above picture, find the following limits (if a limit does not exist, then write DNE): (b). (2 points) Circle the points where f(m) is continuous: -1 0 1 2. (c). (2 points) Circle the points where f(2:) is differentiable: -l 0 1 2. NAME .......................................................... .. 4. (16 points) For the following fuctions, find the indicated derivative (do not simplify): (a). (4 points) f(a:) : 2:43 + “PC—12 +ln(:1:) + 614—2353, f’($) : (b). (4 points) h(a:) = «3:4 + cot(3m), h’(a:) = 23+3 (C). (4 points) w(z) = 111(2) NAME .......................................................... .. (d). (4 points) 5(t) : sin(t3) s”(t) o. (8 points) The position (in meters) of a particle moving along a line is given by: d(t) — -—t5 + 3t —— 16, where t is in minutes. ( a). (4 points) Find the velocity when t = 3.5 minutes. Give units for answer. (b). (4 points) Find the acceleration when t = 1.5 minutes. Give units for answer. NAME .......................................................... .. 6. (9 points) A ladder 26 feet long leans against a vertical wall. If the lower end of the ladder is moving away from the wall at the rate of 5 feet per second, how fast is the top of the ladder decreasing when the lower end of the ladder is 10 feet from the wall? Make a sketch/ identify your variables on the sketch. Give units with your answer. NAME .......................................................... .. 7. (17 points) Suppose that f(:r) = 1‘3 — 32:2 + 9:6 + 1. Show your work! (a). (4 points) Find the crtical numbers of Then test each critcal number for a relative max/min or neither. (b). (3 points) Find the open intervals on which f($) is increasing, and the open intervals on which f(1:) is decreasing. (c). (3 points) Find the open intervals on which the graph of f(:r) is concave up, and the open intervals on which the graph of f(a:) is concave down. (This problem is continued on the next page.) NAME .......................................................... .. (d). (2 points) Find the inflection point(s) on the graph of f(;z:). (e). (5 points) Make a sketch of the graph off(:1:) on the coordinate system below. Label and give the coordinates of the points where the tangent line is horizontal, and do the same for the inflection points. NAME .......................................................... .. 8. (9 points) A rectangular planter of 4200 square feet is to be constructed in front of a garden store. One side of the retaining wall costs $4.00 per linear foot and the remaining three sides cost $3.00 per linear foot. Find the dimensions that minimize the cost of the planter’s wall. Show your work and justify that your dimensions minimize the cost. NAME .......................................................... .. 9. (7 points) Suppose that a: and y are related by the equation my + ln(y) ~ 2y2 : 1. d (a). (4 points) Using implicit differentiation, find 1: (b). (3 points) Find an equation of the tangent line to the graph of my + 1n(y) — 23/2 = 1 at the point (2,1). 10 NAME .......................................................... .. 2:2 ya 10. (10 points) Suppose that f(1:,y) : —2— + —3- — 373/. (a). (6 points) Find all the critical points of f(:c, y). (b). (4 points) Classify (relative max/min or saddle point) the critical points found in part (a)- 11 NAME .......................................................... .. (This page is for scratch work.) — The end - Have a happy and safe summer 12 ...
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This note was uploaded on 01/15/2012 for the course MAT 285 taught by Professor Feng during the Fall '08 term at Syracuse.

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MAT285-2005Spring - Math 285 Final Exam, May 9, 2005 Name:...

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