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a; Complete in pen: MATH 2A  FALL 2010
Second Midterm Exam
Version 1 NAME SIGNATURE UCI ID # E—MAIL ADDRESS .__.. 0 This is a closedbook test. N 0 notes, no cell phones, no graphing calculators. 0 You have 50 minutes to complete the test. 0 Please, write clearly and legibly, and box your answers. 0 Read all the problems ﬁrst, and start with the one you ﬁnd the easiest.
If you have trouble with one problem, move on quickly to the next one and
return to it at the end, if time permits Write down the sequence of steps you would take to solve it, for partial credit. 0 Remember: no cheating will be tolerated! W MMWWw. 1.“:W/WMMW
33::; :33: :
1” 3W
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£33 333:: :3: 33 2 M Problem 1 10 points WW ﬁne and False Questionnaire. 2 points each (1) Let P(x) and Q(a:) be polynomials. If the degree of P is 3 and the degree
of Q18 7, then 3(31_
3333:3339: V” 7:33 3:332:33 :33: 3:333:33; :3 33:33: (3) The function y = V 81 — .732 has no local extremes on the interval [1,9]. . » »\ _ «, f
‘33:: 3333333333: fﬂié‘“ :33“: WWWM 3* 3333 3:333:33 W 33333 m
> M 3333.333: ”WWWWwiwww ( 3W( :3” x 33;) 3:333:33 {3333:3333 :Qé7‘i} 3:3; (4) )If f ”( )  0 then Siﬂf has an inﬂection point at 2
gr\ 3’? 33:3 13:33:: (3,33 39331333353333 1 '3 1533933111 ”Eyﬁéggf , 3S i“ "3 '
(5 ) If f is differentiable arid f (1) f( 1), then there is a number 0 such that]cl<1andf(c)=0.g &?§i;lj 126% €§ Wﬁﬁ 4., 1.3”? :33: 143313;, :33: 3:33:33 Egg 33/33:} 3: WM 5) ’1 f“: i ”93:" “‘3 f f; “ﬁlm ’ ~. 53*?
{9:33:33} K33») [9%] 5.3:} §Q?X wkgg: 3,33,ng if)
,» 3 ,\ K, .3 édﬁii ,: r
‘ . 3 , ,4 ":3 3% W 33:33:33.3: 3:33 333”: mg: 3 33 33:11:33 : 3:333:33, 3:: 3 Problem 2 5 points The volume of a cube is increasing at a rate of 10 cm3/min. How fast is the surface area of the cube increasing when the length of an edge
is 30cm? Problem 3 10 points mi; Weeweo
a (1) If hm f(3:) =2 00, then the line is asymptote
3346‘
for the graph of the function y=f(a:). 2 points
=2: e mm
(2) If hm f(x) = 6, then the line Pi is a majsymptote
x—>—oo
for the graph of the function yzﬂz). 2 points ex: (3) The line #5:” is a, horizontal asymptote for the function Problem 4 5 points Find 3/ by implicit differentiation.
{ V, 2,, \r‘ __ 2 ' r:
f“ \‘. 17 008(1 av )s1n(y) 12. " m»Pbl 5 points ‘3 Problem 6 5 points Find the absolute maximum value and the absolute minimum value of the func~ mm M) = (x2 — 3)3 on the interval [—2, 2]. Note: we are asking for the yvvalues. .. x; X§x 3 ifﬁfw’gﬁﬁ M :2 ant; <32“ 3:?
ﬁg: " Qggwgg €§§x§tfw geif‘éﬁ) 5 oints Use the graph of f to estimate the values of C that satisfy the conclusion of the
Mean Value Theorem for the interval m ’8‘ q ’i‘z ., Problem 8 20 points Sketch the graph of the function f (1?) = :64 ~— 163:2 and complete the information below. 0 Domain: {33%; 333%: 0 lim (3:4 —— 16562) =
$400 . lim (3:4 — 163:2) 2:
33—3—00 0 critical points of f: 25‘ {2’31}
l333% £2::%§i§ 33:33:23? Egg: 0 Intervals where f 15 increasing: £15531 13 {em} 3‘: o Intervals where f 15 decre
{Wzi’jgﬁm E“? \3 1: 23$ 16% \} Wﬂ,ﬂ o f has a local maximum at a: 2:63 o f has a local minimum at 5E 2‘: gig; i . 3611(3)“ 13 :13.» 32 2:: 92% :1 e :::1% O Intervaglsﬁ where fie concaveup: be}; e. 1éf§ fig“ :Q} o Intervals where f 13 concavedown: 1:: E3 .11:— f.» WWW SCORE Q ““7 PROBLEM 1 PROBLEM 2 PROBLEM 3 PROBLEM 4 PROBLEM 5 PROBLEM 6 PROBLEM 7 PROBLEM 8 TOTAL ...
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 Fall '10
 AlessandraPANTANO
 Calculus

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