17bexam1sol - Math 17B Kouba Exam 1< ex Your Name Your...

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Unformatted text preview: Math 17B Kouba Exam 1 *< ex; ______________________________ Your Name : _______________________ Your EXAM ID Number ____________ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page. 6. You will be graded on proper use of integral and derivative notation. 7. You will be graded on proper use of limit notation. 8. You have until 10:50 am. to finish the exam. 1.) (7 pts. each) Use any method to integrate each of the following. DO NOT SIMPLIFY answers. a-)/\/:E(1+x)da: : SOC/4+ x3/22J‘7 : 353M 432x572, c, ) 3 3 ~ éxfiw ~ fix‘flx : 3%?qu 3L glx +4 C)/$($+1)5da: (w M:x+(——»JM:1¢LX W451 Xtu~l) 7 6? : $Cu~l2ubyabvx 13<H6~H574M : ELM-”i.” 4-; b x 1 A 3 5.1. e.) /:L‘2($++2) d3: :2 S[X 4* E14? X+9~1M I #/ CAXCKMN BLX+9Q+ (:x-l : 7w! 'Mxioi 26:1»: 642 — / -,., .L .L- Mx:~az 4¢:«1~—a (L; b/Mx- 1. A+ ek—q- ——aA=’/q) I! l -~~_,..‘- 15A+IA~+”‘/q]&y:zi}'\(></ ax 4%IX+3\I+C. X X1 +a 4+z ,2 “A we“ a a?“ M \uflqfazu'k S‘J—L—LL’I p\&+<.f \ ~quz+g) X I H \‘e “‘8 S[a HA+R&]M :Qu—fva—WE+Q/ ‘._ 2 _ 2.) (6 pts.) If/1f(.r)d:r=3and /02f(:r)da:=—4,whatis/ 1f(:r)d:r? _ 0 l o 2 Lia/ya : ilwwx + Scream —-> 3 : flier/a ~ 4 a iii—w? : 7 -—~ SZJPLXNV = ~7 3.) (6 pts.) The base of a three—dimensional solid lies in the region bounded by the graphs of y = 0, y = 1n (1:, and :1: = e. Cross-sections of the solid at a: perpendicular to the x—axis are rectangles of height 3. SET UP BUT DO NOT EVALUATE the definite integral which represents the VOLUME of the solid. Y \{Z/Q’VLK VvQ: Ste—3%“ A? 4.) (6 pts.) SET UP BUT DO NOT EVALUATE the definite integral(s) which represents the AREA of the region bounded by the graphs of y = x, y = g, and y = 1. .. ‘l _. .f a") Y ‘I x x i AM :513CX’()A7C filial) 47 5.) (10 pts.) Use the limit definition of the definite integral (for convenience, you may 3 choose equal subdivisions and right—hand endpoints) to evaluate / (m2 + 2m) dx . 0 Wiflw) 2’le M311 6.) (6 pts ) Evaluate the following Improper integral: /000 9 + 43:2 dx M - M 4! ._. W~ [ =—fi:t7803ktx‘ ‘,¢eao 30 3 ° -pm<ewawfifi f) Wk» 3 3 3 ~ 4 . 11’ ~ .9: ‘ 3 «1 ~ 3 Tr 7.) (6 pts.) The temperature T of a room at time t minutes is T(t) = (/16 +t OF . Find the average temperature of the room from t = 0 to t = 20 minutes. k AVE— 920—0 g: WM: igowc} lo “370 55M.1e2:3/0(0219 (A) 30 "’ i079: 8.) (6 pts.) Find the length of the graph of y = (3/2)ar2/3 on the interval [1,8]. ~ 3 K6 MQXtagaouXef) y ,, / 5’ 3/9» Z .. 3 :f/E’Ma‘ 15—01 -Mjwrtram 2v? (av 3m 9.) (6 pts.) Differentiate the function F(:r) = / 6‘2 dt. {1‘2 O 3 Féx):SK 6WM+SX+M ~ g: Aa‘ekobk + Sixe {a D &»2 ——5 ! CW 6Lga‘sx) 2- 22 2222 <22 10.) (6 pts. ) What should n be in order that the Midpoint Estimate estimate the exact value of /02( x + 3) 2 da: with absolute error at most 0 001 ? The absolute error for the h2 Midpoint Estimate is given by lEn|< (b — a) 2—4{ 0mg; |f”(m)|}. ’(f $8): M043] 22, tat-awry 3—25454: QQC+3) n (a 3—— 22 222212221: 2222 2:222 = W22 22 222 oéxsz 0£X£at _. g~o _~ A , 1152 W l1~ V1 lelé C2~22 022)“. {W NW} :_ x._fl__/ .23.}:A" 50.00! C / 5(an én Slwk ———-2 The following EXTRA CREDIT problem is OPTIONAL. It is worth 10 points. 11 1.) Use the limit definition of the definite integral, lim 2 f (CZ)(IL1 — {L'i_1) , to evalu- i=1 mesh—)0 , b 1 . . . ate / F d1: . Use an arbitrary partltion a = :30 < :01 < 2:2 < < 33,14 < mn = b for the a interval [a, b] and sampling numbers ci 2 ,/xi_1x,- for 2' = 1, 2, 3, ,n. ...
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