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by: Evert Christiansen


Evert Christiansen
Texas A&M
GPA 3.92


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Class Notes
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This 23 page Class Notes was uploaded by Evert Christiansen on Wednesday October 21, 2015. The Class Notes belongs to MATH 142 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 35 views. For similar materials see /class/226052/math-142-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15
Week in Review 14 15 fzy 1n2zy2 MATH 142 4 8183 Drost7Fa112006 16 ay 51 692 H H H E0 H H F 1 Evaluate the function ay 87z7y2 a 271 b 742 cl 710 Find the domain of each of the following f y E0 i I72y ay 7W ay 312 ay m Find the surface area of a closed rectangular box whose volume is 1000 ft3 as Szyi ewew 7 A company sells gadgets and widgets The gadjets sell at p 250 7 61 7 4y and the widgets sell at q 800 7 21 7 5y where z the number of gadgets sold and y the number widgets soldi Find the revenue function Rzy and the value of R5 6 Partial Derivatives nd f1 and fy for each of the following functions 8 314y2721y 9 fr7y87127y2 0 m y 7 I4 z 1 ay ygj f y 111 12 4y Second Partial Derivatives nd the four secondorder partial derivatives for each of the following functions 3 f y 312 4y2 7 212 f y 6143 H H H 9 H to N ti Minimize the surface area in problem number 6 A company sells 1 logic games at a price p 120 7 21 7 By and y superduper deluxe logic games at a price of q 150 31 7 By a Find the quantity they should sell of each product to maximize revenuei bi Find the price of each product which maximizes revenuei fz y 41281yl6y Find the critical points and label as a maximum minimum or a saddle pointi 212 7 212g 6y3 Find the critical points and label as a maximum minimum or a saddle pointi 4x2 em 2 Find the rst order partial derivatives fag fyi ln 312g Find the rst order partial derivatives fag fyi Maddy sells two types of homemade preserves and the weekly demand and cost equations are p15075110y 427515174y Czy 400 81 12y where 1 represents the weekly demand for jars of peach preserves and y represents the weekly demand for jars of quamquat preserves p is the price of the peach preserves and q is the price of the quamquat preserves and Cz y is the cost function a Find the revenue function Rzy and evaluate R20 30 b Find the pro t function for Maddy7s peach and quamquat preserves Pz y and eval uate P20 30i Byfold Blinds Inc has a productivity function de ned by 1201392y393 where z is the units of labor in thousands and y is the units of capital used in thousands Currently the com pany is using 25000 units of labor and 30000 units of capital Find the marginal productivity of labor and the marginal productivity of capital 25 For Byfold Blinds7 Inc to maximize productivity7 should labor or capital be increased Math 1427 Calculus for Business7 Fall 2006 Texas AampM University Review for Final Exercise 1 Find the vertex form of fx 75z2 10x 7 3 Exercise 2 Solve the following equations 2 ln2 7 3 lnz 6 ems 2z24z39 Logx 5 3 2 4H1 lnx73 lnz2 lnx for z gt 3 Exercise 3 What is the domain of fx lnz 5 3 7 x What is the domain of g m7 Exercise 4 fa z25 ifzlt1 fa 3x74 1f1ltzlt4 f 72216 if4lt Find lim f lim f 7 17 7 1213 M 1311 W hm we 7 NEW W 7 4 ls f continuous at z 1 at z 4 2 7 1 Exercise 5 Find the limits lim L 3 73 z 7 2 Exercise 6 The cost of manufacturing z bicycles is Cx 500 10x 7 001 0 Find the change in the cost from x 100 to z 200 0 Find the average rate of change from x 100 to z 200 0 Find the instantaneous rate of change at z 100 Give an interpretation of this result 0 Find the marginal cost function C Give an interpretation of C 200 Calculus for Business7 Fall 2006 Texas AampM University 0 Find the exact cost of producing the 201st bicycle 0 Find the marginal average cost function Exercise 7 Let f be the function fx xBz 4 0 Find the equation of the tangent line to the graph f f at z 1 0 Using the four step process7 nd the derivative of f Exercise 8 If f1 3f 1 57 93 7 g 3 97 91 0911 27 nd h1 for f z 96 0 2 90 x f96996 M 2m Exercise 9 Find the derivatives of the following functions we V35 5 37 we f96 96 i 05964 i 37 3 7 2x z2 7 4 xz 1 95 m Exercise 10 Let f be the function 2x3 95 Use the strategy for graphing rational function to sketch the graph of f Show that y z is an oblique asymptote Exercise 11 Summarize all the pertinent information obtained by applying the graphing strategy for polynomials functions and rational function and sketch the graph of the functions 995 96 1396 5 h 3 7 z 25 39 3 NC 95274 Exercise 12 Find the absolute minimum7 the absolute maximum of f z376z29z2 for z 6 055 Calculus for Business7 Fall 2006 Texas AampM University Exercise 13 Find the maximum volume of a cylinder box with no top such that its area is 7139 square feet Exercise 14 Given the cost and price demand equations7 Cz 100 e4 750 and p 10 e4 0 Find the maximum revenue 0 What is the maximum pro t Exercise 15 Find the derivatives of the following functions Exercise 16 The price demand equation is p 15 7 001 0 Find the elasticity of the demand 0 The current price is 10 Should we increase or decrease the price7 in order to increase the revenue 0 Same question if the price is 2 Exercise 17 Find antiderivatives for the following functions 1195 i 3 2x2 1195 my 0 h 7 3 Exercise 18 Find each integral 0 z3x2 7 59dx 1 o mzxxS 2dz 0 3 o xxx 7 1d 1 1 2 oze 3w dx 0 05 m 7 36dx Calculus for Business Fall 2006 Texas AampM University m o idz v3 7 z Exercise 19 Find an antiderivative F of f 2 e2m such that F0 1 Exercise 20 If the marginal cost is MCx 100 7 01x 6 Find the cost function if C10 2000 Exercise 21 Given the function f 101 7 e O39Zw Find the average value of f over the interval 050 Exercise 22 Given the function f e w2 on the interval 0 2 0 Sketch the graph of f Draw the rectangle from the left for n 4 Evaluate L4 and give a bound of the error between L4 and the area under the curve 0 Draw the rectangle from the right for n 6 Evaluate R6 and give a bound of the error between L4 and the area under the curve 0 For which values of n is Rn an approximation of the area between the curve and the s axis within 01 Exercise 23 Find the area between the curves y xem2 and y z for z in the interval 01 Exercise 24 If the price supply function and the price demand function are p Dz 100 e O39Sw and SW 10 esw 0 Find the equilibrium point 0 Find the consumers7 surplus at the equilibrium point 0 Find the producers7 surplus at the equilibrium point Exercise 25 Find the rst order and second order partial derivative of the functions 0 ex 7y 0 xy ln lny o 273zyy35 o lnz 7 5y Exercise 26 Find the critical point of the following function Are they maximum minimum saddle points 0 3x2 72xy74xy25 0 3x2 7 3y2 7 Sxy 0 3 2mg 75x2 7 2f Calculus for Business7 Fall 2006 Texas AampM University Exercise 27 Given the production data for the years 1990 to 1999 car 0 Find a quadratic regression equation for the data set 0 Estimate the production for the year 1994 and the year 2006 0 Find an exponential regression equation y a bm for the data set 0 What is the best model 0 Estimate the production for the year 1994 and the year 2006 Math 142 Exam 2 Review Marl NI Week In Review thlem Sal 7 Review In um 10315 534143411151 lnxlruuur Jennwhix ald 1 thn ma pacedde equzuunp 7 0 0qu 50 a 31155 the demand x as a mclicu or he pricey F o u I 0 3 I 5039 P 12 had we clasucily of dtmnnd Hp I Ef 39 quot wlonr 39equot39 f x39l t 8 act ims we BOA Io IOI as 395 50 ID Ilo 39 QWVK 1 1 itquotle 63 asCIS mu 24 m u 3quot in dcmand swagaw WWquot 4 who 3 I I bunl aw 4mm 177 Indemand u m Elm 53 JIM lq gt a 1k pun I M q 3 a I07 5amp3 a in II 5 b1 il dhxdldunno Math 142 Exam 2 Review 1 39 39 39 1I1133161n1whcrwisyears since 1990 Find mainmum robbc cs m 200 year 1995 1996 1997 1 1993 1999 2001 21101 zaoz per low population 54 514 41 40 36 31 23 2 nndnver K We rutoquot MG 1 x l Wall ml 09 W In m In Iquot I l 3 Mm 3939 Mt riui339 3 he 39a I L 410 ms in 4 n 3a1 m II 1134114quot u3311m I 3 u quot3 1h 1439quot 5 11111 Math142 Exam 2 Review 3 Find the derivalives ofthe following functions DNS Do 1101 simplify It HUI TB 5 gx 39Ia T abu uf BLx39 xh TI we zhs lzs ws wuwkw a xT 3 lawn 39 639 e T t n b 13 au39dhll h 1 xingquot hh un g lawshhlqbs f a 13mh 21 3943th Mb I n nnhm 3933 Qua1V5 Hid u Nous0 muf ns 1 hr Math142 Exam 2 Review b gx10g5 x4x23x71 73M DNS a l h T 0 L5 439 I 39 39 3 Fl a 55 Jub 9nd I 1 a l d he 16 31 n z 13561 3 5 3 quot3 m 9 3 7 ws 344 is 73 d I B fhsz nb 39 33 my mx mm 7 h 39 6 ruins W 37351731 Math142 Exam 2 Review c hxeh 7xm3ftx m wt 4quot 3394 13quot a d i 45quot 39 3403 e2a1 4 F b a b It 39 E Infn Jquot as 41 gt nn 3 xv a v b 5I 313 h39 39 3 x M39 A gin I HM ef uhb in M Math 142 Exam 2 Review 4 Find the intervals WheIe fx ixze increases and decrea 113 inc nu Wk 1 I 1 v aquot thA deguses Wuquot 39539quot mghik P E39 quot k I grin rec Y a l t Oixf xia 9 3 v quot 32 quot 11 Mu m quota i in W 239 x f 53 a o m as Wquot 3 IIP quot39 lavasums Wat3W mama ltM165 I v m wotev m3 Math 142 Exam 2 Review The following mc nn has lelali 13 ivyum W I 5 Jam wlw n Errq 1139I mam max AA ull w an nlmlm m d xnz xq A u LINGMG vf wk 36 quot00 A 15 Lemma dun vim5 quot 5 n U r U 9 1325 o 39 325 1 add 5 3 Math 142 Exam 2 Review 1m e If hm and s4andf 5 f0 a Findh39 5 39 bus 8 39 06 TI ix 639 k llst Srr l J Jnlg WI 39 B 39 I t h39lsxdmi L hh 5 39 51 3 quot32 1612 b Find the equation ofthe line tangem 10 mg at x 05 3 M t quot b m s W 3 an K c I 5 g In Jam W 3m IIoa 2512 s b 8s391b asuu 5 Math142 Exam 2 Review 7 Sketch a graph of a function that satis es the following conditions H Orzv f x gt 0 01172 0 f xlt0 on7oo2 and 0 Do I f x gt 0 on 70071 and 1 no f x lt 0 01171 1 1Efx01ii fxw WW 7 N 1 5m 20 A U NNnnrmw 392 n D 39 32213 Math 142 Exam 2 Review 8 Use the graph of x below to answer the questions that follow 3 F 57 F P 9 rs as y ty u 5 Identify the intervals on which f x is increasin 2 Identify the intervals on which f x is decreasing o dhu H93quot 1quot3 3 Identify the intervals on which f x lt 0 arc 0 quot93V 1 V a 3 Identify the intervals on which f 39 x gt 0 a 35 u H 3 Identify the x coordinates of the points where f 39 x does not exist KIAI 0 3 Identify the x coordinates of the points Where f x has a local maximum at II 5 Identify the 39 coordinates of the points where f x has a local minimum x1s Math 142 Exam 2 Review 9 Suppose we function Ru sox4 1 zepresems the revenue function for a company in huusands cfdnllars when selllu a me Lemm quot items m 1 imms I U 39l S 1 I15 a 0553 quot 153 avg M St Chiba W saog v 23 9quot a w 39 V I 239 15 b m1 mew average revenue funcnoll damhue of anquot m M VI rum 5 1 a 5039 41quot Math 142 Exam 2 Review 10 Use the Wm nd the derivalive of fx i x1 I x thud 13 I39vIo h I 6940 13 Wm aouwxgm lrlm lm 1H HM Hourus mum 1 1k I I L l l h 1IYIWO hMAjf x I I h 39 aw 39 E 39 Mamu 39 u ihb I 1 3quotquot My 39 it who 39 mum a bu I3 Math 142 Exam 2 Review 11 Given f39x 38 7 3 use derivative techniques 10 nd a the intervals Where x is increasing and decreasing b Mo m 7 7 325330 I 1 1 no I 39 31 139 35 3S393 33334 0 B a 4quot 39 s 3 dmgIu3 E b relative extrema of x HA mu 339quot cu n m 1 c Ihe intervals Where x is con ave u and concave down M v39 it 3 3 H5 quot W33 gm L 73 quot quot39 6169quot 1 0 W 001 D no n h d all points of in ection 1 0 Math 142 Exam 2 Review 1 If Px1ooH 7 500 produced and sold m1de is m a F d Lhe marginal pro l funcn39on P a too2m 3 Find HIE anroximms grgf gb a39ggd flux pmducuug 11m 3 Hum w 5 x I amp V134 I003 l I go 0 s 49 W Ha u Iiooo C levelmf cms Would Lhisbcia wiscquotIImVefur E mpnnyu makc39 Vi39hy nrwh umni P39lssS looalssS 00 no o My 0 now am bums menan palJin Ncl 4 55 mil In h M W M I on quotm Math 142 Exam 2 Review 13 How lougwill it take money 39 39 39 39 mminnnn lv 9 1 64 1 4 quot on 091 ohm 1 N W Math 142 Exam 2 Review 14 In a Computer assembly plant a new cmyloyce on avemgc is able m assemble Nu1ourz 7 units a crl days ofcn lheJob naming a Winn is Hammer 1 dawn 5 days N m Io we t3 0 3 Ine a m quot39 ll e N39f I LIE I 35 unih N39 s Him 393 suans N39lt 415 JR qt L2s a 4e 3935 Ht 5 9 MB 5 39 e 1 ID 5 539 Jn i3 411 a in 3 t 3 3 33


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