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# 211-unknown-02fafin - MTH 211 FINAL EXAM NAME_— Dec 20th...

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Unformatted text preview: MTH 211 FINAL EXAM NAME __.______— Dec 20th 2002 Circle your discussion SECTION: Ozgun Unlu, MW 7:45 Ozgun Unlu, MW 8:50 Nicholas Ehart, MW 9:55 Nicholas Ehart, MW 11:00 Prashant Patel, MW 12:05 Prashant Patel, MW 1:20 Ben Marsh, MW 2:25 Ben Marsh, MW 3:30 1. famibdm=§—%lnlax+bl+0 2- fmdm:adibcln:::g‘+c 3. [mdx=adibc(gln|cm+dI—gln|am+bl)+C 4. ﬁdm=gﬂ\$§g§§m+0 5. fﬁdmzln|m+¢m|+0 ’I‘rigformulas: 005(1) +y) = cosrr - cosy ~— sinm - siny sin(a: +y) = sinzc - cosy+siny - cosm Problem (21 pts.) Find the following integrals: (If you are using integrals from the front page of the exam, you must identify at each step which one of those ﬁve formulas was used.) sin 2:1: b / d ( ) cos 2:2: 1: Problem 2. ' (9 pts.) The demand :3 (in thousands) and the price p of donuts boxes satisfy the relation: 302:2 — 22:10 + 4:1:p3 = 520 Will the revenue of the donuts distributor increase if he raises the price when a: = 1 and p = 5? m2+2 Problem 3. Let = SE — {B — a) (5 pts.) Find the domain of f b)(8 pts.) Find lim f(:::) {Ii-+00 x2+2 2:1:2—5x—3 wax/H —5 c)(8 pts.) ‘Like above, let f = . Show that the only zeros of f’ are: m: (In other words: ﬁnd the zeros of the f’ (as), and check if your answer coincides with the given one) d) (8 pts.) Show that 3:2 + 2 —— > .5 29:2 — 5:1: — 3 "' O for all a: > 3. 2 2 Use the fact, that the only zeros of derivative of f = h (found in part c) are approximately equal to —3.39 and 0.59. Problem (9 pts.) Find and classify the critical points of the function: 1 4 1 f(ac,y) = §\$3+§y3+§\$2—2m—y+7 Problem 5. (9 pts.) Newton’s cooling law states that the temperature T of an object after time t changes according to the formula: T“) = To + C ' 6]” where To is the temperature of the surrounding and C and k are some constants. Suppose that the temperature of the cup of coffee obeys the Newton’s cooling law. If the coffee has the temperature 200°F when freshly poured, and 1 minute later has cooled to 190°F in a room that has 70°F, determine when coffee reaches a temperature of 150°F. Problem 6.. (9 pts.) Find the solution to the initial value problem: y’22ﬂ-lna: y(1) = 9 Problem 7. (14 pts.) Find the following derivatives: a)—Ciln t2+3 dt t—12 b) __ (e sinw) ...
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## This note was uploaded on 08/08/2008 for the course MATH 211 taught by Professor Onlineresources during the Fall '06 term at University of Wisconsin.

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211-unknown-02fafin - MTH 211 FINAL EXAM NAME_— Dec 20th...

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