Advanced Math Archive: Questions from July 19, 2023
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1. Which of the following functions \( F: \mathbb{R}^{3} \rightarrow \mathbb{R} \) are linear? (a) \( F(x, y, z)=x \) (b) \( F(x, y, z)=y-2 \), (c) \( F(x, y, z)=x+y+3 \), (d) \( F(x, y, z)=x-y-z \),
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1.29 Considere el conjunto universal
U ={1,2,3,...,8,9} y los conjuntos A={1,2,5,6},
B={2,5,7}, C={1,3,5,7,9}. Halle: (a) A?B yA?C (c)AC yCC (e)A?B
yA?C
(b) A?BandaB?C (d)A\BandaA\C (f)(A?C)\Banda(B?C
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Encuentre la linealización L(x,y,z) L ( x , y , z ) de la
f(x,y,z)=2x3+y3+z3‾‾‾‾‾‾‾‾‾‾‾√ f ( x , y , z ) = 2 x 3 + y 3 + z 3
en el punto (1,2,3) ( 1 , 2, 3).
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