quiz09_soln - Math 155 Quiz 09 Name#— Instructions This...

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Unformatted text preview: Math 155 Quiz 09 Name: #— Instructions: This quiz must completed without the use of notes or books. You may use a calcu— lator. Write clearly and show all steps. 1. (2 pts.) Are the following mathematical statements true for a, b, c, d E R\ {0} (If a, b, c, d are real numbers different from 0)? Write T or F (for true or false) in the space provided below. (a+b)c=ac—1—bC a(b + c)d = (ab + ac)d r a d:— fora>0 2. (4 pts.) Consider a dynamical system given by TV . xt+1 = ismfirt) for cc 2 0. Find all equilibria, and classify their stability using the first derivative (hint: the above is a transcendental equation, meaning there is no explicit solution for lOOK ‘COV m‘l’USErflx‘OhS of K€+15X£ anal 3415.”; [31:57A(X¢\ HT '3 1 M2 attuT/férbc 3. (4 pts.) Let f(:n) = 2:03 + 3(23 ~ 2)2 be defined on the interval [—3 : 3]. Find and classify the critical points. Find the global minima and maxima. £/(X‘§ “:— 6X2 4 6(K‘Z\,( W 4mm rule I H X2+><—»z\ *’ C(XHMX—D CmLfml PM“: 56% Y -* ‘7— fl’qzzl 4:03:32 M: g ' «Gaza? é X5! <99 (:(x‘) TS HM allobq/ MIAFMLJW‘ and W3 or #235 1’3 Me. alobql MAW/mum ...
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This note was uploaded on 02/21/2008 for the course MATH 155 taught by Professor Johnson during the Spring '08 term at Colorado State.

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quiz09_soln - Math 155 Quiz 09 Name#— Instructions This...

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