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Math 121 Exam 3

# Math 121 Exam 3 - Exam Three MATH 121 Fall 2007 Name...

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Unformatted text preview: Exam Three MATH 121 Fall, 2007 Name Section Show all your work on the exam paper, legibly and in detail, to receive full credit. The use of a calculator or any other electronic device is prohibited. You may only use technigues discussed to date in class. l) (10 points) Using implicit differentiation, ﬁnd dyfdx , with y deﬁned by the implicit relation sin (xzy) : x 5m [ﬁg/)0) ; A. COS[XL’a//)O>'[LX‘9'+X18/A)2i ﬁx“ / (0 5 (>39) 1f, _|____ 02. / X3“ (OS/#31) 2X3 /5 2X3 +XZE11/ =3 2) (10 points) If y : u3, u : sin(l), I: all}, ﬁnd dy/dx O Outsq3=(\$mﬂ)js 5’s; m a [/é ( dX iii-die 7? :61n/(7>)3 -t/L x. 2 BML-Cosﬂl-éx £_:3gzn/F)COSZF‘):>< ~‘/ ‘ a. 39/12.? Cos ﬂJ‘iK L E 36M [0?» (05/0?) /% ‘5 3sm‘ﬂ7) 605((7i'1LX i Z X : i. ant/(’2?) (05(5?) 3 ! ———#——- \ ‘ lof7 lx : l Exam Three MATH 121 Fall, 2007 3) (12 Points) Oil spilled from a ruptured oil tanker spreads in a circle whose area increases at a constant rate of 6mi2/h. How fast is the radius of the spill increasing when the area is 9mi2? 4 L ﬂ 61‘ q 3 ?«7T( 7T“ F ”—7 F7— / WI 2 g :— zﬁ'rrﬁ/g’ ) H7" ”7”“ MN 2of7 Exam Three MATH 121 Fall, 2007 4) Find dyfdx . Note: you do not have to simplify your answers. 4a) (10 points) y : ln(l — xex) 30f7 Exam Three MATH 121 5) Find dyfdx . Note: you do not have to simplify your answers. 5a) (10 points) y : x210g2(3 — 2x) 5b) (10 points) y : tan’1(x3) l':: l " Li; :*C it a / 4. [[XBH L : 4,—st /+)<4 Fan,2007 40f7 Exam Three MATH 121 6) (8 points) Find dy/dx. Note: you do not have to simplify your answer. Hint: Logarithms. y‘ (x+1)(x—2) ”1&5 : /n /5M[><)> +“/m/(osx> +//) ”3?) — /’i [)<7‘"/) I/o /K~L) L- , _. l / M' 3/: (”X 4— SMX +37 3 9/196 605% / 4,. )<#L{ 7<>'2/ { 5/49C (05x (7 5‘0 6: / ”TI/n66 (K+/3[X’&3 005x ,_ smx +1 _/L y / gmx (DJX L X X}, “” Fan,2007 _sinxcosx u'rx “IL/ﬂk) 50f7 Exam Three MATH 121 Fall, 2007 7) Consider the implicit relation y2 + xy — x2 — 5 = 0 7a) (10 points) Using implicit differentiation, compute % . ([email protected]+Xgﬁ)’2x"5£“5 1:293/11'37LX8/d; :5 8‘ [23711] 3 1‘3 z z 9‘8 g /L9+K) 7b) (5 points) What is the slope of the tangent line at the point P = (1,2)? 6of7 Exam Three 8. (5 points) Fact: lim haO MATH 121 4h—1 h derivative, to compute the derivative of y : 4’“ Cf [x740 / %>( A [PL/M by/«ao )(" I: >( eh? ~¢ Lbn 5:7t;eao /% "" ptaab ALI»? §LX [ﬁék‘i> FaH,2007 : 1n(4). Use this fact, and the ﬁmdamental deﬁnition of the Pr Pts Sc 1 10 2 10 3 12 4a 10 4b 10 5a 10 5b 10 6 8 7a 10 7b 5 8 5 70f7 ...
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Math 121 Exam 3 - Exam Three MATH 121 Fall 2007 Name...

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