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Unformatted text preview: Name: MA 1021  2007 A Term Section 2
October 2, 2007 Quiz — Sections 3.9, 4.2, 4.3 1. Consider the function: = 41c5 + 5x4 — 40x3 +17 Where does this function cross the yaxis‘? On which intervals, if any, is
this function increasing? On which intervals, if any, is this function decreasing? (10 points) a): Crosses yrams where 70:0 1%) —=— 17 F’t’x): 20x4+ 20x3w120x7’
':— (20x1)(7£"+ W‘é)
:— Q20x")(7£+3)cx~l) 972:)“ O @— "3; 2‘20 (Men/a»! 20x7— x+3 x—z Sign inc/dec. I
C__ 3) o) + + ..  decreaxlvy
( o, 1) 4 + __, — decree: smj
(1)4'0“) + + + '4‘ tariff—eats}?? 2. Use the linear approximation technique we studied this past week to
approximate each of the following. (5 points each) a. 9.93 (note: actual answer 13970299) L{q.a) 5 loco + 300 {emu IO) —= loco30 Lﬁﬂzﬁm b. 282/3 (note: actual answer is 9. 2209 to four decimal places) Mac): ffM't 707“) (“a”) '5" 0L; 2.6
__1/ 7_ 42(50: 27 a C?
47(5) = 35)‘ 3 "3 / ,3; :2;
PfaLvE’ZT c7 LL/zg‘): qi (Z?*_‘Z’i)_ [17.5) =.. a. 7.227. 3. . 0’
Given the following equatlons, ﬁnd an expression for —y (6p0ints each) dx
a. x2+xy3 =3xy+3 2x+(l)(y’7)+ X(3V‘§l—:)= 3q+ 3x35; b. ysinxzleny égfﬂx +ycosx :. lxﬂnytIXZ 1—4:!)
dx gl‘nX“XQ> (£1 :: QX’Q’Wa" by”? 4. For the curve described by ex + ey = em) , 21. Give an expression for 3% (J0 points)
x )F X4
62 + e 41 1: e Y (1+ 4:1)
oh: x
My x
r y x+tg\ aleI __ e —._ 6
Le " e j x
X4
41 e L 6"
4x 6)!” emu, dy b. Give an exact numerical value for — at the point (In 2, In 2) dx 
(2 peints) j
'(P dues heme ) 5. A rectangular box has its dimensions changing at differing rates: Its
width is increasing at 2 inches per second, its length is increasing at 3
inches per second, and its height is decreasing at 4 inches per second. The
box is currently 6 inches wide, 4 inches long, and 18 inches high. a. What will the dimensions of the box be two seconds from now?
(2mm) angular: 502:: [D ' A :2. ,8 g l8—(1)(‘t) = no 6t 03(2) é " " Nam: 10 b. At what rate will the volume of the box be changing at that time? Note that.“ = + + (8p0ints) =~ (armaun comm» + 0°)00>(~‘+> "3‘ 100 139/
, Sec, W71: :,,m I’x Io” 6. A: \liéozwsga" : {00 males agart A car leaves the city at 1:00 pm, traveling north at 30 mph. A second car
leaves the city at 2:00 pm, traveling east at 80 mph. At 3:00 pm, the
driver of the ﬁrst car notices a large hear at the side of the road. a. What color is the bear? Explain your reasoning. (2 points) 1} Would be very thEch my; *0 jet
1Q” credié “Er the; fch'hion ' I b. How far apart are the two cars at 3:00 pm? (2 points) W
80 c.. ligw fast is the distance between the cars changing at 3:00 pm?
pomts
2_ 2 7..
Z Z "~: X: 'l' '7
x 4...): = 6&1 :' all» at
End. 43' When 2: “50 ‘Ftcm
51+ 7"" 30 «Love
» ‘2: 60
2.2. {if .. 2% AX + Z 4—3
. 0H" J? 7 at—
az My iolvwﬁﬁ (6°) ~32. it
..—~ :— —— 't’ F“ ' f“"‘_" "“ 6 a in“
01+ 2 01+ 2 at “>0 ﬁrm160(2) w? *************** END OF QUIZ **************** D ...
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This note was uploaded on 10/13/2009 for the course MA 1021 taught by Professor Tashjian during the Spring '08 term at WPI.
 Spring '08
 TASHJIAN
 Calculus

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