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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(glncm+dI—glnam+bl)+C
4. ﬁdm=gﬂ$§g§§m+0
5. fﬁdmzlnm+¢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’22ﬂlna: 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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 Fall '06
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 Calculus

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