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Sol-165E2-F2007

# Sol-165E2-F2007 - MA 165 EXAM 2 Fall 2007 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 2 Fall 2007 Page 1/4 NAME GM‘ D l N —————‘ Page 1 / 16 10—DIGIT PUID ____* Page 2 /34 P 3 26 RECITATION INSTRUCTOR ﬂ—L Page 4 / 24 RECITATION TIME TOTAL mo DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one. . Write your answers in the boxes provided. 4. You must show suﬁicient work to justify all answers unless otherwise stated in the problem. Correct answers With inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators or any electronic devices may be used on this exam. 0:) (16) 1. Find the derivative of the following functions. (It is not necessary to simplify). (a) y = (1 + cos2 ac)6 u PC 3% 1» c3 x+w§xfzmsx L—SW) d” < KOTﬂ -—~. cake-2am". @449 J K 9:. (c) y : sin2(3aé) a; Q sinﬁﬁwsfiﬁzl he , ah}?! I: 23p, L r a , (d) y = 1n(ac4 tan x) M a» #9:,» (ﬂange + 4%??ewai <“"" " 4 x 2r d)! tom r: mm Q; =es’ém‘x—rfmftwﬂ ., —c7 ‘2) \$1- 3. +4.»- gsfx “0/ x _ X Eahx MA 165 EXAM 2 Fall 2007 Page 2/4 (I (8) 2. Find d—y by implicit differentiation, if {rzy + 133/2 : 3:3. as VZALIL+ 2X? 1—W2‘33i‘il4—gzz3 X Ln ....... “WM! 7 @ C?) (8) 3. Find the second derivative of y = \$629”. d’l : wewz +£M (in 0.. 2;: 2‘): 01%, :1, 7333.2 +e 23+26 6176?” 2x 2.7: a 4—): e + 4 e E1 (12) 4. Find the exact value of each expression. . _ 1 _ ' _ r!” “54 E (a)sm1(—E):\é<ﬁ@ sm\3_~.ﬁ; zf‘glré2 _, I, If r 4 (b) sec(tan‘l 2) '3 SQ!» U} wi 11“ Let up): tom 2. 4:) Tantéz’Q ,ar’fé ‘3 “is; or“ “ “M FA} twig-r1 36.5% .9 mwé :ﬁlz‘m 2W? ‘ 3 {5% \J‘ . 57f "9 liming-33mm. (C) tanwl (tan Tr 3%; G d cos 10 2:; .u- t, at»? () ‘3 c2) Cmsxéwﬁ) I, giggly.” :3; 22» 6‘ 2 I? 2‘ 2 W 3 (6) 5. Find the slope of the tangent line to the curve y : sinha: at the point (In 2, and express your answer as the ratio of two integers. %= :2 003% x ': ﬁsiiéjx I 2 t. a , M 3%} xqgng: emf ﬁgwr‘ : ‘5 32%;" 4» MA 165 EXAM 2 Fall 2007 Page 3/4 (12) 6. Find the derivatives of the following functions. (It is not necessary to Simplify). (a) y = tan—1&2) NFC Eli — 4- <2V>< M (Way—>24? l s. 'Z'X ~01” "“’ 7f r (c) PM -—~ 65:“ 3‘: em” M W “x dx 7i 2352 G .. gag/W J.— ..QQA :21: 7 23—931 __.. 2‘6? '2. X (6) 7. Find the linearization L(a:) of the function f = x5 at a, 2 1. LR): £61) + NQMMQ) K aft/A = \$0) + We (vs a») e“ *2) §(i) :3. (8) 8. Find the differential dy if (a) y = v1 + 9:2 <2. *1th (b) y = sec(3a:) OLE} : EXCBX) tom '3 d3! Fall 2007 Page 4 / 4 MA 165 EXAM 2 (12) 9. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 In higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/ sec, how fast is the boat approaching the dock when it is 8 In from the dock. L‘LI X [01, tide/r, (ivigjéamce 69% m Emmi Wm mud 3 he, W 0/ QM," WILL ©i¢€Aﬁ f¢.¢m/§£C 1:in WW X33??? 3 _ on“): M "We (12) 10. A coffee cup has the shape of an inverted circular cone with height 10 cm and radius at the top 5 cm. If coffee is poured into the cup at the rate of 2 cm3/ sec, how fast is the coffee leg/e1 rising when the coffee is 5 cm deep? ﬂew 5 ﬁnal ‘ mm, "— my.1w-““21.0-1.1?!” L QJJC \( \OQ Wk v0 0 We k~>\ ‘3 , ,gM;:Q :2... 637” cm/ sec The coffee level is rising at the rate of ...
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Sol-165E2-F2007 - MA 165 EXAM 2 Fall 2007 Page 1/4 NAME...

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