Past Examination 3 with Solutions - Calculus Techniques | MATH 1100, Exams of Calculus

Download Past Examination 3 with Solutions - Calculus Techniques | MATH 1100 and more Exams Calculus in PDF only on Docsity! Math 1100 Sec. O01 FALL 2007 - Exam 3 “SY Instructor: Francesco Strazzullo Name. Instructions. Only calculators and an index card are allowed on this examination. Always use the units of measure in your answers (when applicable). If you use the substitution method, be clear showing your choice for u, the steps for computing dz and (eventually) x. If you use the integration by parts method, be clear showing your choice for u and du and the steps for computing du and v. SHOW YOUR WORK NEATLY, PLEASE (no computation, no evaluation). USE CALCU- LUS, NOT YOUR CALCULATOR. 1. (18 pt) A new pizzeria in Salt Lake City models the demand of its pizzas by p) = D(x) = —30x + 80, while their supply is modeled by pe = 5(x) = 527. Find the consumer and producer surpluses. ~ 5x. 30x tf020 D5 (2% 6X- Io) 20D (x- 2\(x+te)= oz pee Resetev <0 y 52 og B EQvir mew PRoderlor; T(x) = S(x) @ -20X+h0 5 5xo D @ [ EQUBRWUM PRICE - Be SOx) = 5- 2 = 20 2 |. Cons. Svar. . [ae “Pp, dx = |: 30Xt §O- a0dw = _ | wxrsodee oO & 2 - nisx° + 60x | = 60 ‘® Xo (6) . PRodvdeR suas | 20x - 3 ey = 40 -£ oO ; 2 p.- SG) xz |20-5x¢de = 1. 240. $0 3 4 Solution: E8.-€O pS.= 2. (16 pt) A car-washing company finds its Marginal Profit to be modeled by the function aoe where 2 is the number of cars washed and the marginal profit is measured in dollars per cars. Find the change of the profit P when 2 increases from 5 to 8 cars. 8 A ASKES FoR [P(8). P5) = Clan @| tg -3x¢)" (8)-F) Le ThEw (3)/ P@)-PG) = | p= [ Satara > > a YEW ErDRwWTS 2 Ku. gDuz-191 re -191 -I4 ()| 8-0) | x aH 2 4 [wide = [ ures 6X é Py -?y : 191 -) (\P ofa . i(-+): iS) | = 1[ 4 8 ayy #4 , ry 27 tu= 9) 2 - 27. Solution.. 5. Compute the following definite integrals: (a) (16 pt) (#21, pg 450) 3 [ «(20 —3)* de = 2 ® sande pu du ) 2 veel THEM : yes : wz 2x-3% PB: 5 (wt? pei? z (9) yew grote 1S q yep SY I oe “l 2)) 1(8(3+3)-0 (+2) Q 2 66.9% Solution: (b) (16 pt) [= dz = etd x / [ ~ z pe 6) Cant Fretow xe th SYATH. DIZ, XH Keel ea ax = Qo +l i 2 z - (6) | Betis | xe pd = x + dale | - & ln x el o R x x “0 gyat. wR Lore ‘ Qulé gilé ial qt Lt fag - Bt 2 Le ba = 2 a [192 1GF Re Solution: