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MTH132-Test4-Sol - Page 1 2008—11-26 Name(Print Clearly...

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Unformatted text preview: Page 1 2008—11-26 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Test 4 Dec 1, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [5 pts each]. Find the derivatives. é , £60 A p f \ r x 05 ‘ ~ - = ‘ m ~ (g .- flaw) - an 0 I y ': v'kéx y/qu- sulfa 0 : QW‘X 2. [6 pts each]. Find indefinite integrals. (a) I4xxll+2x2dx (42f ‘t; I+23<2 , go off, i jq’? alt 3.. . 35/2 : fat/WC : %(l~+2><)/+Q I I 4:. x ..K >< Page 2 2008-11-26 3. [7 pts each]. Evaluate the definite integrals. 2 (a) x(1— x3)dx '3 ‘7' . 2 2 0 1 fl 2.. » 2 l 3‘ ,- ‘ ,_,_._ .. : .. : S ““XQLNK '5 [31X ' SKL “(.2 g 0 ' s ,0 71/ 2 (b) IQ sin3x ‘ cos x)dx So/dhl. 1cm: 25‘IL3x-zesx ; k . ‘ 2 .. fl _ _. / ‘ {’(i-x) : 25‘,L3’(-y) ~(a’SC-X) c 26%» 50 [6X - 2 fo my if» a wax w/r/ , 2/4 rs c~ éy/wW/C WW, 7/}. ' ,Tyg/ SJwAm 2 . (at f : at“ I O/f : CLSX‘O/X ; ‘ hV‘ > ‘A ’»'¢._ J Z’tg‘pzf : 3:75} ‘1 : Jiltfl 3L0.) - D —l Page 3 2008—11-26 4. [12pts]. Letf(x)=x2—4x+3, 03x35. 5 (3) Compute If(x)dx 0 " , g i2? MS” ’— 2' ~ ‘ - A .. g: c—-—-‘ > _» ,5 «2x +5>( 9 , 2) ~—- 2x2§ +/§ 5 -53’ .. i2"? ‘ fog, _. 22. “ 5 «5 ’ .5 5 [12 pts]. Find the area of the region enclosed by the curve x = y2 and the line y = x. Maw {‘ ,‘mtz‘nyz‘flm [mm x 7:5 , ycx ,(f away” (“QM/’8” ‘/*: fie} [53‘ - x5); ”23> as e ‘i 4" i X L. >< 1 I Page 4 2008—11—26 , 3 4 [10 pts] Set up a Riemann sum approximation to the integral J(x2 +1)dx by partitioning the interval [1,3] 1 into 4 subintervals of equal length and using the left endpoint of each subinterval. (a) Evaluate this sum. . _ L-QQ 3»! { AKA”)? “1‘17?” :3 ”(k‘: (Rf/KIN: I + Ck 1 qu C DWI/tat 7‘61, $71” euogf'fi ) , - lit—H 2, f 2 (fif/aba k )7 “’4 vi“ XI: ...
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