quiz_05-key - Exam Course Duration Due Date Instructor 16s...

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Unformatted text preview: Exam Course Duration Due Date Instructor 16s MATH 2451 quiz_05 Multivariable Calculus 25 min 2099-02-10 (Tue) McCary T.C. Use KEZ (First Name) (Last Name) 2016-02-12 16:23 1. (10 points} Let. f : (T233192). Use a linear approximation from to estimate f Hint: the exact. _ 1.2 2.52 mlue 1:: f (21) — (—2.97) you'le [45,ng TD Jr?be ‘FWM )917 (1,1?) = (3% (3:? 204-12 HQ 15 Fgécugr DIFF (31‘; comm/n; mmsz m rooyNoMrM) ] 60 m = [own gum) \\ ‘ AS a 8‘?» I ” so WM) = $6) + [mwflzUIm-m) jmo m comma“ HA5 «Mach/Minot: wE’u, remosz/é. Teanxuc. 2 2. (10 points} Let. f : (GI + 3*; My (a) Find all values of a such that. [Df is Singular. [Wm] T” 4] aj Md [019(1)] : [9: L] T emauL/ua <1=> = o (b) Find all values of a such that. [Df has determinant. 1. dbt[2m l] :1 L a afi—w ‘4 Qua—Ov' = O of 11W ' 9(a) 4H? 3. (10 points) Let z E (C be complex, z = 3: + rat. 0 1] has the property J2 = —I (this should remind you of 2'2 = —1). (a) Show the matrix J = [—1 0 2 _ 2 (b) Notice the function f : (332$; ) encodes the (C —> (C function z I—> z2. Show that matrix product of Df I and J con1n1utes. 3‘} KTHE 6AME 4.__’—j (c) Notice the function g = encodes the (C —> (C function z I—> z*. Show that the matrix oroduct of D9 I and J does not con1n1ute. 3‘} X mm D43 3 Eva?!me ¢ 1);? coMMuTES w/: J ‘(3 :5 amen ymwwmc m (MW/rt. WIS IS gremlw/ 12ELMED m OItFmEm/H 110M 0F mom: a.) a) wugqgluomm , :1 Is P0991814 1b“vrv:pg 67 A vEc’rorU (“Wu/“‘6‘ (M49360: w/ (@617?) ...
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