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10Se1ics - Prof Girardi Math 142 Spring 2010 02.11.10 Exam...

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Unformatted text preview: Prof. Girardi Math 142 Spring 2010 02.11.10 Exam 1 MARK BOX class PIN: _ -_ — (*) Extra Credit: 5 point for knowing yor PIN number. INSTRUCTIONS: (1) To receive credit you must: (a) work in a logical fashion, show all your work, indicate your reasoning; no credit will be given for an answer that just appears; such explanations help with partial credit (b) if a line/ box is provided, then: — show you work BELOW the line/box — put your answer on/ 1n the line/box (c) if no such lme/ box IS provided then box your answer (2) The MARK BOX indicates the problems along with their points. Check that your copy of the exam has all of the problems. (3) You may not use an electronic device, a calculator, books, personal notes. (4) During this exam, do not leave your seat. If you have a question, raise your hand. When you finish: turn your exam over, put your pencil down, and raise your hand. (5) This exam covers (from Calculus (ET) by Stewart 6th ed.): Sections 7.1 — 7.5, 7.8. 11.1 . Problem Inspiration: You were warned. example in class homework problem § 7.5 # 9 homework problem § 715 # 15 homework problem § 7.5 # 21 Handout of 100 integrals # 35 homework problem § 7.5 # 41 3"??‘15592"? Hints: (1) You can check your answers to the indefinite integrals by differentiating. (2) For more partial credit, box your 11 — du substitutions. Honor Code Statement I understand that it is the responsibility of every member of the Carolina community to uphold and maintain the University of South Carolina’s Honor Code. As a Carolinian, I certify that I have neither given nor received unauthorized aid on this exam. Furthermore, I have not only read but will also follow the above Instructions. Signature : M You, wart Wamfzi m,- We #34: écw’ (:3 f‘%~;:. gemgéa Fill in the blanks (each worth 1 point). f—‘fz' : 2233““ we . 29 [£0 isaconstant wda > Obuta¢1,thenfa"du 2 gffl Q: +C7 fc'osudu: {HUM +0 I sinud-u f can'udu fcottuiu " fsecudu : ‘ fcscudu ~ fsecgudm 3: ”3y?“ +0 fsecuttmudu 2 5E 60“ +6? fcscaudu : "(OEU +C joscucotudu 2 ' {Ac} CM +3 4—,? '1 1.4L Ifaisacontantauda>0thenfmydu := 0“- a“ g; +C‘ Ifaisacontmtanda>09henfmdu— 2 59,9.4 f; +17 Ifaisawntantmda>0thenfmdu— M £5 ‘SESQJ‘ Q +0 Partial Fraction Decomposition If one wants to integrate L— where f and g are polyonomials and [degree of f}- > {degree of 9} then one must first do (éQffi d 1“” £10 a Infiegmtion by parts formula: f adv = H ,‘V (y; gig Trig substitution: (recall that the integrand 15 the function you are integrating) if the integrand involves a2 +u“, then one makes the substitution u 3 i 3 1:43.? E ’e' Tzig substitution: ‘ if the integrand invoivas qz—uz’, then one makes the. substitution 1; z a. g 3 34.3- Trig substitution: if thginbegmnd involm 1:3 ~a2 than one than the substitution u‘ = U“. S Q96. trig formula“ .yuu: answer should inmlve trig functions of 9, and not of 29: sin{28)= Z 5 “’16 com { g ’1‘ C O 5: 1‘6 ) (M ) trig formula. since cos“ 9 Jr sin' 9 :— 1, we know that the conwponding xelationship beween trig formula ., your answer shutdd haw cosflfl) in it: cos‘w) — 2]"; l 2 trig formula” your answer shouid have c0599} m it: 5812(0) z: angentfic tanland cantfie sec)is ‘ +1é{yf6;8%zéfl . fig ~fl g RADIAN S . {ycmr answer should be an angle) \ arcjmn (-0 3 ‘ 1% [‘4' Hint: ”from problem 1 come in handy. Sstx 44L :7 A“ S (\—ca$2—X> A?“ 4. m—l ’5 d = ._L ’ 2 cc +211) L Hint: m2 + 2x = $(a: + 2) = (:1: — 0)(m + 2) XII _.. —A— + E...— :: «(1%) , 15 x11). 5;» IX" :- AOXA’Z) +89% 9/ \ :‘2. >2 12.44 +§ ’X 3 MUCH" Jr ’7, 3/2. +0 5a. Complete the square. The two lines should have numbers on them. The box should have a plus or x2—4a:=(x— 9— )Zl:l l minus sign in it. l, «Ax +‘1 /sec3mtan3:c dm = 1—...— ww.w.~\ w ”@9 W3“ *ng * = M m2? (m Wm WM kn...._,,‘..~.~,...,.....‘...“ , 36+ in mes 9% v ' Y‘" 5 ' ...
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