Sol-165E2-F2006

Sol-165E2-F2006 - MA 165 EXAM 2 Fall 2006 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 2 Fall 2006 Page 1/4 NAME GRADING KEY Page 1 / 16 10-DIGIT PUID Page 2 /32 ' P 3 2 RECITATION INSTRUCTOR age / 8 Page 4 / 24 RECITATION TIME TOTAL / 100 DIRECTIONS 1. Write your name, lO—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. 3. Write your answers in the boxes provided. 4. You must show sufficient 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 or calculators may be used on this exam. (16) 1. Find the derivative of the following functions. (It is not necessary to simplify). (a) y = 6—57” cos(3:1:). CL -5 ' l ' x 6-5315) 3:34:13 yésmfixD'j +CDS(3 ) Npc ~3 6,5,5“ {3X} —- S e’SXC’OSG‘ X) (c) y = ln(1 + 2639:). ole _ 4 263753 f"— e3)! dx 1+2 (d) f(:1:) = \3/9 + 8sin211: :(9+3 sin2x)"3 '2. {/00 -_= 3%.(91- ‘3 Sin2x>‘=€ 8(033‘29 2 MA 165 EXAM 2 Fall 2006 Page 2/4 at (8) 2. Find (1—: by implicit differentiation, if (tan y)(sinx) = (By. [@anallwfix) +(%i"><)(5ec Wit. = x 0% + \} --_..... g W14 64 Beiiw) 58.62%, «X1 (ti—3; : ti-ltm‘lflwsx) 6) 00.3 __ ‘5 ‘(tom‘3743‘05’0 of} .— (Sinx) 5e33, — 7f (12) 3. Find the exact value of each expression. l3: (b) sin(sin—10.7) :: 0.7 0.7 6) .1 (c) tan—1(tan $315) :: Tam 1*} (:4) tang—:(i ) Ji< 641E -— E. 3 (3) (d) Cos—1(_%) =L9 (4;; Cos L9: — i2 , 053 err lé s 2.! 3 213— ® 3 (12) 4. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y = tan“1 fl N PC (l. _ Jaw—4 fit: (X‘JQZ‘FR 1 L‘LN (5“) l? k @ 9f" 2 \l‘; (x-n) (b) me) = sin—W) I - :1 2, W- m x [ n21...” @ (C) y = (x+l):c : e-eh 0&1)“: ex Q/h(x+.t) %= Exp/HGH-llG '1— + Rafi”) MA 165 EXAM 2 Fall 2006 Page 3/4 (8) 5. Find a formula for f(”)(:r) if f(:17) = -—'l Q (2‘) : (X— ’3.) fag) : — 1(x~1)‘z g(2)00: 1v‘2.(xv1)—‘3 6% = — 1~2'3( ><-1)‘4 (4) 6. Find an equation of the tangent line to the curve 3/ = sinha: at the point (0,0). t3: eihk x NPC éfl.‘ =1 , I OWL: ‘3 '7‘ 1E (5) 7' If 17(17): f(9(-’r))7 f'(1) = 5» and 9(17) = 62*} find F'(0)‘ I I / - ,' F (x) ': (c305) (36¢) = We“) 2e“ F’m)=.§’(1).2.1 7.6.2'1-40 , @ F<0>= w [a (6) 8. Find the linearization L(:17) of the function f(:1:) = (sina: + cos :13)3 at a = 7' 1.00:- {m + Mamba) K = gap tax—1:)” (gm = (Sinw flow): 5.0;) :4. §’(X)= 3(Sinx+m$x)1(msx—Sinx) {’(Ig) = 3.1- (A): :1 (4) 9. Find the differential dy if y 2 sec(5:17). NI : 82.4520 tan(a3x)i5 olx MA 165 EXAM 2 Fall 2006 Page 4/4 (12) 10. Air is let out of a spherical balloon so that its surface area is decreasing at a rate of 2 cm2 / sec. Find the rate at which the radius of the balloon is decreasing when the radius is 20 cm. Let Slum SUN- (ROM MT“ km. W chnM'w') o/tL} bmgfloowu Giwam: 0L6- _. __ 2, ch/mc d1 ’ (3 Find. wlvun V2200”). CD :4TH‘1C’D a9_ a mflflaca \Nl/ULM T:20.‘ -2: 81120:“; 52:3,? Cm Sec 11- ‘” @ .___2:..a» Cm sec [72“ (5017 "" (12) 11. A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? ‘ P X B ilk-“WW” Givzh 9.9::4~2fl :‘3Tl‘ VMlS/mu'w 0U: (79 W 3 / Irma % Wm ><-=’lkm TOLW9=—:— €53 ‘5 29.3 25$}— ec d): 3 ax CED e0 . 7F— km/mm E ...
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Sol-165E2-F2006 - MA 165 EXAM 2 Fall 2006 Page 1/4 NAME...

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