2AsecondMSOL - e g a Complete in pen MATH 2A FALL 2010...

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Unformatted text preview: e g; a; Complete in pen: MATH 2A - FALL 2010 Second Midterm Exam Version 1 NAME SIGNATURE UCI ID # E—MAIL ADDRESS .__.. 0 This is a closed-book 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 E 3. 33333 £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 concave-up: 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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