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mid1-a-2009-sol - MATH 1300—MIDTERM lu2009 d I-D IS This...

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Unformatted text preview: MATH 1300—MIDTERM # lu2009 d I-D-# IS: This midteI‘In exaIn consists of 4 multiple Choice questions and 3 long 3.11— -ns. The multiple choice questions are worth 5 points each, and the long answer e as indicated. The total value of the exam is 60 points. insurers to the multiple choice questions in the boxes below. All your work on ‘wer questions must be clearly marked. You may use the backs of pages. answer questions, YOU MUST SHOW YOUR WORK CALCULATORS. NO BOOKS. NO NOTES. teed additional scrap paper, it will be provided by the proctors. E :3 E lhoice Section Qtlestions (1—4) Calculate: 1_ 1:3 m 27 112.13% :1: W 3 ) 18 C) 27 D) 36, E) The lixnit does not exist. ,.__—__._. 1?. 7. QV-EDsz-t— 3 x +3) 3:. z _ 2. § . .1 x 2:, CM x +3x+5 .-.-— 3+5.x.°>==’2.? “R ‘ “'7 5—..7 3 Find the equation of the tangent line of the function f(:L') = (217 ~+— 1)\/ 3.7: + 1 _i B) y=§+§ C) y=%——Z— D) y=%+% E) y:23x_% 16;: + szg '3 'Z '5er 2-5- —VH_ 3— g z: “(—t- —" —— *— 4” 2.01? H R 1'1 = 5 r ~+ ‘9 5“) é: 2.5-1:. ‘9 a.) b: “-7:- '1 ’ =- 31" ——._1.. a *9 q L, 5 Use implicit dfifi‘erentz’ation to find 539.:— at the point (2,1) for the equation: N a?! u l m \\ \/ U u t A .. 'i! M~ = Find the inverse of the function: 2 A1 f(:L-)= :+3 B) it? C) 9:53 D) 33?: E) grist—i .— I __ _ 5 =5 ‘2 i, 3*; —=> “TV-0 ~ 2‘7 ‘ > my?" 3 :5) X)—— 2—3 =':— —‘_3)‘ _\ —-3>< 7 ‘9 =~ ‘27-: ver Section Questions (5—7) L (12 points) Using only the definition of derivative as a. limit, calculate f’(a:) 1’06) 3 (3 — 2902 &C>r+4x2-— QC“ ( 3—2Ck+42))1 -—-C$-—Zx)1 A}: ‘Aw-‘I I” 1 — 2(k&dk))1: 3- I2er42)+ HCx-ndx) 0)..n_w_ 1241—4, sz+§xAxau kgsxf‘ \I Z. 5v2x) = ‘5—12x 4:- Rx.)- LCkx-Ak) )1 — (2'2”)1 " 4k+Hx1+ ohm“, £4492 ) — (2-42»: «FLU—z) 3 x +— QxA-‘k— +- H(AK)Z ;.fl_'({ L20”; . ~124k+ QkAx-k “(4x37- :6 Ah m —~12+—S’x+‘-¢Ax a. —-('2.+9x k—bb r Mkwt—‘l-'\ ' gr‘éj go? ()LwS) 1:“? Lu... I r c4 “LJa... 3(45 of“ Lawn i (14 points) Suppose that a deposit of 3,000 3 is made into a bank: that gives Suppose that interest is compounded 6' ti’rnes per year. rats) Write a, formula for A(t), the value of the invest’rnent, after t years in this hats) How much will the investment be worth after 3 years? rate) How long will it take for the infuest'rnent to triple? (P _ C( +_ :— )vvt which Lg—QMS 6 2,,” -(—:-. '5 *— (7'0" 9:: chm; C‘s/recl— 0. a“: ‘S’ g-‘fm 1 2‘ be .. gnoco C‘ 4' ‘ sabfiawF-Z—S- 647 «so :— %m (t“" 2:25.) -—- 3“"; 3 ‘- ((+D.o$ ‘+ f b 3 _ 4+4“ (w °~—-—“;" — 3r“ \a. ’7 7 "1' 4, t... (we-{F '>"” -— 21'" ' (14 points) nts) A business sells 5,000 radios per month at a price of 300 dollars each- It mated that monthly sales will increase by a level of 50 units for each 2 dollar se in price. Find the demand function, as well as the revenue function- nts) Suppose another business makes burglar alarms. Suppose that there is a fixed cost of 25,000 dollars. Suppose each alarm costs .90 dollars to make and Le manufacturer has set a price of 150 dollars per alarm. Write down a profit >st function, and deter'rnine the breakeven point. a_...¢,£—:-a (a : Deg) Ewe—«m 4a.“... L ($.90 , ease) Mel (369—2 ,sne—e 47a) ) C259 ‘ gag“) 9—? 7- - 4 M: Ax :— ~€o = 25' z. “727");- + b VL'S is. (=5 ‘ D 29‘ __ .._1'i_ + goo ._ 1; 1 ~Gm.) :-_-- X(DCZ¢7 =— x- (7 :— — +g0°k _ 15m + 90x BrML—GVL-s -‘ ’ ?Cac)='— ‘3 -) [953): L 631‘ r. 2;.“6 ‘5’) :. RC3“) ‘— CC") = 603‘ -2.-S'.°°D 3‘. 3 16:, uni-cs- astion (1 point): Name the two historical figures who can both claim to have culus. Lv-J‘L'on. k L/Q‘tbulre _ Space for additional work ...
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