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Unformatted text preview: Name: MA 1021  2008 B Term Section A02
November 7, 2008 Quiz — Sections 5.2, 5.3, 5.4, 5.5, 5.6 1. Evaluate each of the following antiderivatives. (4 points each) a. I sec x tan xdx c. I 2 dx 2&(X+'7)+ C
6L yam1)" + c
Was—W 1 3x
d. J36 dx #e3x+c c. J [ IZHdXJ dx (bonus question; no partial crediv .. S 02er6de : ﬁx2+c'x+c= Cl and C1, are 6:2 (“5ka 0 I . Solve each of the following initial value problems. (6pofnts each) a. —=x —2x y(3)=4 be t u q, 3. A ball is thrown straight upward from 18 ooblongs above the surface of Mars, with an initial velocity of 16 ooblongs per second. (An
ooblong is a unit of distance). The gravitational pull of Mars is equal to 4 ooblongs per second per second. Answer the following questions
about this Martian ball. (4 points each) a. Express the velocity of the ball as a function of time. b. Express the height of the ball as a function of time.
2'3: Ie—LH: a = W— 2+‘+ C
4% Jm=meeaw c. How lon will it b unil th bll hits teoun‘? N
5m :0 a) —u‘+ [an ISr—O
(*1)('l7+l)({—ﬁ);O {’S—I d'L 62‘," (“a2 ball 0"” anurol
in secMal d. How far will the ball have traveled in tht time? Be sure to . I
count the entire distance upward and add the entire distance ' downward. = i 'y(~r)= 37.+é'++l8 = 5‘0 Frombtb‘t, +Yl~¢ls 56435??— rwmtiba, Puts sh 32+?” gi 4. You have estimated the area under the increasing function f(x)
between x=2 and x=7, and above the x—axis, by using ten inscribed
rectangles of uniform width, as shown below. Your estimate is 35. Now you would like to estimate the same area, but this time using ten circumscribed rectangles of uniform width. Given that f(2)=3 and
f(7)=10, what is your new estimate? Show your work. (6 points) Us‘tnj Circumsrnbeal ReﬁtAsh: lh 'H‘NJ' Case
Neda} u5mj rial!” £452. 17‘ij «AF 6“? Lap" +0 Ae‘i'Prvulne “fish[’5 a? E°XE;. 6
5. Use Riemann sums to evaluate: [(96  3) dx (16p0ints) 6. Evaluate the following integrals: a. 3(x+3)dx X24
2
x 3h __ %
3+3” m " (V's) (5+6) 1: 3é”8 ...
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 Spring '09
 Abraham
 Calculus

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