quiz_05 - .0 F05/045/o1 0 Use T.C 16$ MATH 2451 quiz_05...

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Unformatted text preview: .0 F05/045/o1 0 Use T.C. 16$ MATH 2451 quiz_05 Exam ble Calculus 1varia Mult' 0 0 Course 25 min . 0 Duration 2016-02-10 (Wed) McCary o u Due Date 0 o Instructor E W. , w W A M I W©@@@@®@®®@®®©@®®@®@@®®®®® . . r: \ r. x x!) :3 .f‘ IL©G®©®®@®®@®[email protected]@®®©®@®®©®®®®©®@®®® . Net ID [email protected]@@@@@@®@@@@@@@@@[email protected][email protected]@@®@®©@@®fi (First Name) k [email protected]@®©@@@@®©®®©®®®@®@@®@®®@@®®@®@®®® V @®®@ ®®®@ C, We“. @ @ © @fi. ® @ @ ® my ® \ xix [email protected]éaxeseaenwsea®@@ea k Fax ./ NJ _ see @aaéeesse seemsaaeeela m, a xfiv émaw a , O I:eg®©ee®®@®@[email protected]@®®@@@@®®®®@[email protected]®@@@®®®®@ w®®® @W 0 (Last Name) 2016-02-09 19:51 1. O. F05/045/o2 Q l (10 points) Let = ($23: yz). Use a linear approximation from (2) to estimate f Hint: the ex._ TIM f (52?) = (—3133) ~35: 1!} *3}; {ix/A 2 it: 2» Edi‘géi‘Nfi—é/ 27:3 2‘20 27$ ' 9¥ a _ "27'" '25? v10 / 23;, . 1-79,! «X I 9 W {We/70) 2-429 . 7( [ fix] 4 ¢ ‘27] 7'”; ' {WI/17 ) Lem. F ‘flflé 01.6 éerrflmwp 8 PpeA-gé- pow“ : 9- .2%“: H Tmilé 0F!" [5 IIIL? —4~J[ a] _ _ 5—! D- }? (ilfi "[2 mm 2 _ - 37?? ¢"‘ ' 27+ 0. S 11;. :% 0 : 3 O >5 J, Grader Only J, 063 ©®©®©®®®®®Q O. F05/045/0L . . (10 points) Let f = 3’). ' r 0' '- L 7 7 (a) Find all values of a such that [D f ié singular.- (b) Find all values of a such that; [D f has determinant 1_ ’f ll n . * [Kl [j :- #L‘M‘A‘g" 5:5 :I K k x ,2é‘x f" fa— : l l Grader 01:11:,r J, .. FOS/O45/O4 . 3. (10 points) Let 2: E C be complex, z = :1: + fly. (a) Show the matrix J = [ has the property J’2 = —I (this should remind you of 2'2 = —1). J: a] «I 0 —la [OJ * ' I 2 _ 2 (b) Notice the function f = (32$: encodes the (C —> C function z t—) 272. Show that matrix product of [D f and J cornnmtes. J 3: “‘0 ‘ r t 1"“ “is” "—3 " P“! K 5“ ‘y i ' ,JJ . _ I 1 )Efi 0; it fix/r 2] 2% i J ‘ ’Lfl“ “V ”‘ ’1“ 2%J (hmmuré (c) Notice the function g = encodes the C —) (C function z I—> 2*. Show that the matrix product of . [Dy and J goes not commutex r f f if I, 1* ,7? '7" 4” 7" ND tr! 03 M 79)} Ii 1 ” W ' ’ a; (1 0' "@113 PE) I] Hang in J Am uji UR [p4/klgjtl 0 1/7 iGraderOnlyJ, . O® @@®@@©©®®® . ...
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