Math 149 - 001 -002(circle one)Exam 2Name:/IPal!e 1 of 5Dr. P. D. McCra28 March 20061. (20points) A page of a book is to contain 27 square inches of print. If the margins at the top,bottom, and right hand side are to be two inches, and the left margin to be one inch, find thedimensions ofthe page which uses the least amount of paper.(a) Draw and label an illustrative diagram.(b) Write one, or more equations, expressing the relationships between the quantities.(c) Express the unknown quantity to be optimized as a function of one variable.(d) Use the techniques of calculus to complete the solution of the problem.I ~kJ ~I oj, . '..L- - ~~'-"::)~A~~i ~ ~ (~It=If'Wh~~~If & -'" B ~ ( II -'f) (/IV- 3) -:::.-;;1..7- t4t\ _~ ~~~--5-fj(~ ~~ I~ (CO) ~ w=~~~~H ~~~~i:X.I (1+-~)(X-3) -:~7-J~1-1:; 4- + ;) -=1-/ (?(-3). T~ ~ I'} =- f-(,c)-= 'X (L{+ :JT((?f-3))= I..{X.J-;)..7-~?C-3(d) ~ £I'J{) =-Lf I- (~-~)~7-) -;r}.1t-(/)( 1(-3) 2-f If}!); I{ - ~ I -= 0 ~ ()(_,) -z.::: [!. ~(X-~)2 4,y _2 ::. + 'I 'V~ 3+!. . Po.3_' -,~ ~o" -;1 - 2:. ," - z. ~ 2. - Z~~~~ ~:3+~:.!f'= T{ := W1-1-: 'I + z. =f. -= '-f.,.. z.~ = l..f-l- "2~ ~ '1-1- 3 I 2 -:::. / {:>!.:!-3 ~-~ ~"2.-T~ -b4(~ ~ 7-~ ~~ ~It!} ~~b~ :f//rXJ= +-(j~-z..)1('K-3)3 >0 L(J~~ X=.IE~l~ ~"trY1~~~.Math 149 -001 -002(circle one)Exam 2Name: JDr. P. D. McCray28 March 20062. (20points) Find dy ifdx(a) x3+y3=3XY~ ~'J ~~'~'VYI ~q/-e..:it~ ~ ~~~tr3X'" i- 3i'"~ = 3["/- + x~l~ 3f-~ _3><;:;= 3;;-3X2..('J2-rx)4:: ~_X2..~~_ ~_«2._;;lic - ~2._~(b) xsin(y)+ ysin(x) =1I ·~ 'I -+ )( CU)1 t1d' + f1' ~)( +~~ k :: 0(X ~'t +~ x)'j-' = -~~)<-~'1-,;' ~ !!:l--::: _~ CP:JX +~:/>tPx )( ~tJ -J..~ ::rMath 149 - 001 -002(circle one)Exam 2 Name:l/ .!1:!Pasze3 of 5Dr. P. D. McCra 28 March 20063. (20points) Find the derivatives of the following functions.-. -'-- -/(a) (5points) I(x) =2arctan(3x) ~ /) K .~ ~.:;:f I('K1-:; ~ I -". (3)::: ~I +(3X) Ii-'X'2-/-1+7(?-.(b) (5points) g(x) =4arccos(5x) ~~I(?C):: 4- - I , .(5)-y/ -(t;X) 2../.)-/x~ )(~- I11'I_X2.1-- -(c) (10 points) hex) =~ arctan (2x3)I,3x2-f(I of 4 %'~) -I~ (:l.>t') .Math 149 - 001 -002(circle one)Exam 2Name: A/IEPage 4 of5Dr. P. D. McCra28 March 20064. (10points) Find the most general antiderivatives of the following functions.(a) I(x) = 4 -=- 4- .f. J)1+ x2 (/ + )(L( F('JC)= 4 ~- I '?( +-c. J I--R.e-. ;=-~)C)= ;/-/)<..).¥ 6-r-x)=J..fkv.. GI tK) =dfx.).5. (lOpoints)Find h(x) if h"(x)=sinx+cosx, h'(O)=l, and h(:)=;.h'fX)-= -~X+~}(-J-CII ::. ~' (0) -= - ~O + ~ 0 + C I -.::.. -I+-O + C,~ C, = ~ ~ h/ r'IC)::. - ~'Y +-~)(-I-O\,.hIXJ= - ~ X - ~)(' 7-;l. K + C~Jf=:-h(:!fi)==-~!f-CP?+ ~(!f)f-C"L~ !!:z..== -~ - [J. +-7!: .J- C., ~"2.. Z. 'Z. -./'\ - r'Z rz: ..r::'- -:z..- -::z:7-- ::: ,z-'2-Math 149 -001 -002(circle one)Exam 2Dr. P. D. McCra28 March 20065. (20points) A car is traveling at 45 mph (that is, 66 feet/second). On dry pavement with tiresin goodcondition, when the brakes are fully applied the car is capable of producing a constantdeceleration of 22 ft/s2.(a) How long does it take the car to come to a stop when the brakes are fully applied?(b) How far does the car travel from the time the brakes are applied to the time the car comes toa full stop?a 1-1::) = -z.z. -::. D-t, v f-b}v (-6-) = -2...2.. t; +c, -=. b1: 51-1:::)(,(, -=vI 0) -= -2,Z (0) +C1 ~ C, =- ,?,S (b) -= - 2:2.E..'2-. +- (, (" -t -=-- II t:'Z- +- (,t, i=2...~~~_~ S{f))~ (kM!~~~~~~~~.t,f&~ ~~~).V ( f:s~) -:= 0 ~ - 2..2-6siDp +" '"-654= ~::. 3 ~'2...-z...S (3) = -1/. L~)z..-+ be, ,(3) =-11 "f-Itf? =-99(b),',~ ~ ~ qq /-SJ_~~:k~ ~~~.,,
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