Port A Folio .mat.1

  • November 2019
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Portafolio N.1

Iparte 1). f ( x, y )  9  x 2  y 2

D  f  ( x, y )  R 2 / x 2  y 2  9 x +y+1 x-1 D   ( x, y )  R 2 / x +y+1  0,x  1

2). f ( x, y ) 

3).g ( x, y ) 

9  x2  y2

D   ( x, y ) / x 2  y 2  9 4). f ( x, y )  16  x 2  y 2

D   ( x, y )  R 2 / x 2  y 2  16

IIparte Limites. : 3 xy ( x , y )  ( 0,0) 5 x 4 +2y 4 R  0; Eje x=0;Recta y=,No Existe.

1.)

2.)

lim

lim

( z , y , z )  ( 0,0,0)

xy +yz+xz x 2 +y 2 +z 2

1 (No Existe). 2 (Discuta la Continuidad): R  0; Eje x=0;Recta y=

f(x,y,z)=

xy tan z

R  Dom f(x,y)=  (x,y)  R 2 / x. y  0  f ( z )  tan z





R  Dom f(x,y,z)= (x,y,z)  R 3 / x. y  0   f ( x, y ) 

x .e

1 y 2

R    x, y   R 2 /  0, +  

 f ( x, y , z ) 

1 x +y 2  z 2 2

R  Dom   ( x, y , z )  R 3 /( x, y , z )   0, 0, 0  

2

,

2



Determine el Dominio: 1.) f(x,y)=x 2  y 2 t2  4 t

g (t ) 



R 

x2  y2 x

2



2

 y

4

2

2.) f ( x, y )  3 x +2y-4 g(t)=ln (t+5) 3x+2y+1  x 2 +2y 3.) f ( x, y )  y Ln x R=ln



g ( w)  R 



e w +1 w

x 2 +2y +1 y Ln x

e x 2 +2y yLnx

2 x +y xy 3 xy R  f ( x, y )  2 x +y

4.) f ( x, y ) 

f ( x, y ) 

x2 y x 4 +y 2

5.) f ( x, y )  g ( w) 

x 2 +2y y Ln x

e w +1 w

 fog 





x 2 +2y yLnx



+1  

 x +2y  e g ( f ( x, y ))  g    x 2 +2y   y Ln x     y Ln x  2x+y Sea f(x,y)= Encuentre f(f(x,y),f(x,y)) xy 2

 2x+y  f  f xy  2 x +y 4.) f ( x, y )   xy

f(x,y)=

f ( x, y ) 

x2 . y x 4 +y 2



 2 x +y   2 x +y  , f   xy xy      3 xy f ( x, y )  2 x +y 



IIIParte. 1.)f  x,y   f f

4 x 2  y 2 .sec x

 x    4 x  y  2  Tx   y    y.sec x.T 4 x 2  y 2  2

2

b.) f ( x, y )  Tan

1

1

 y   x  

y x 2 +y 2 x f ( y)  2 x +y 2 f ( x) 

2.) f ( x, y, z )  y.e 2  y.e x +z.e -y f f f

 x   e 2  y.e x  y    z.e  y z -y z  x . e +e   Emprendedor: Joel Soto C.I: 18.546.451 Ing.civil “2” Prof: Deibys Boyer.

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