Camara

Personal information

My name is Rafael Barrera, I am twenty years old, I live in maní casanare, I am student of industrial engineering in the cead Yopal , my number of group is 90008_545, my favorite color is green, my favorite sport is tennis. I like pop music ,my favorites singers are celine Dion ,susan boyle and andrea bocelli.My dream is to live in australia with my family.Places to visit
The Bandola park is a magical place surrounded of Four Lions and many birds in the sky. Is the bandola more big of the world.



they are many the hotels in mani, the hotel Cusiana is the more beautiful, where you can swim and enjoy in family.

The are restaurants elegant and striking. The typical food is veal Llanera.
you can enjoy thegastronomy Maniceña every day. Peoples from mani helping visitors to buy crafts of wild animals.
I think Mani  is the most beautiful city in the world, is imposing, charming and welcoming. It's great to go on vacation.
The beaches are fantastic and people are very friendly.
I recommend visiting this beautiful city.



e^x-e^y=x+y


e^x-e^y=x+ye^x-e^y=x+y










FASE1


Hallar la ecuación de la recta tangente a la curva:


〖y=Cos 2〗⁡〖x para x=0〗

f(x)=cos2x

〖f (x)〗⁡〖= -2 sen 2x〗

mt=f^' (0)=-2 sen (0)

mt=0

Ecuación de la recta tangente

P ( 0,1) mt=0

y1-y1=m( x-x1)

y-1= 0 ( x-0)

y=1


〖Si h(x)=x/√x halle el valor de〗⁡〖h" ( 3)〗

2. sea h(x)=x/√x hallar h´´(3)
h´(x)=(√x-x 1/2 x^(-1/2))/(√x)^2 =(√x=1/2X^(1/2))/X
√X/X-1/2 √X/x=1/2 √X/X*√X/√X=1/2 X/(X√X)=1/2 1/√X
h´´(X)=[1/2 (X)^(-1/2) ]^´
=1/2*-1/2 X^(-1/2-1)
=-1/4 X^(-3/2)
=-1/4 1/X^(3/2)
=-1/4 1/√(X^3 )

f ( x )=〖sen 〗^2 2x

f ' ( x )=2 sen 2x .cos⁡〖2x.2〗

f ' ( x )=4 sen 2x .cos⁡2x



FASE 2


〖f ' ( x )〗^ =(lnx^3)/(lnx^5 )

f(x)=(lnx^3)/(lnx^4 )=
f´(x)=((ln〖 x〗^5 )(ln x^3 )´-(ln x^3 )(ln〖 x〗^5 )´)/(lnx^5 )^2=(lnx^5 ((3x^2)/x^3 )-(ln〖 x〗^3)((5x^4)/x^5 ))/((ln⁡〖x^5 )^2 〗 )
=ln⁡〖x^5 (3/x)-(ln⁡〖x^3) (5/x)〗 〗/((ln⁡〖x^5 )^2 〗 )
=1/x (3 ln⁡〖x^5-5 ln⁡〖x^3 〗 〗)/((ln⁡〖x^5 )^2 〗 )


5. f(x)=x/e^x

f´(x)=((e^x )(x)´-(x)(e^x )´)/(e^x )^2

f´(x)=(1-x)/e^x

6. Hallar paso a paso la cuarta derivada de:

f(x)=e^x ln⁡〖x 〗f(x)=u.v f(x)=u^' v+u.v'
f´(x)=e^x ln⁡〖x+ex/x〗
f´´(x)=e^x ln⁡〖x+ex/x+ (e^x x-e^x)/x^2 〗=e^x lnx+e^x/x+e^x/x-e^x/x^2
f´´´(x)=e^x ln⁡〖x+2ex/x+ e^x/x^2 〗
f´´´(x)=e^x ln⁡〖x+e^x/x+ (2e^x x+2e^x)/x^2 〗-(e^x x^2+2xe^x)/x^4
f´´´(x)=e^x ln⁡〖x+e^x/x+ (2e^x)/x〗-〖2e〗^x/x^2 +e^x/x^2 +(2e^x)/x^3

f´´´(x)=e^x ln⁡〖x+(3e^x)/x- (3e^x)/x^2 〗+〖2e〗^x/x^3f´´´(x)=e^x ln⁡〖x+e^x/x+ (3e^x x-3e^x)/x^2 〗-(〖3e〗^x x^2-6x e^x)/x^4 +(〖2e〗^x x^3-6x^2 e^x)/x^6

f´´´(x)=e^x ln⁡〖x+e^x/x+ (3e^x)/x〗-〖3e〗^x/x^2 -〖3e〗^x/x^2 +〖6e〗^x/x^3 +〖2e〗^x/x^3 -〖6e〗^x/x^4

f´´´(x)=e^x ln⁡〖x+e^x/x+ (4e^x)/x〗-(6e^x)/x^2 +〖8e〗^x/x^3 -〖6e〗^x/x^4


7.
lim┬(x→0)⁡〖(cox-1)/(sen x)〗=lim┬(x→0)⁡〖((cos⁡〖x-1)´〗)/((sen x)´)〗
=lim┬(x→0)⁡〖-(sen x)/cos⁡x =-sen(0)/cos⁡(0) 〗=0/1=0

8.
lim┬(x→2)⁡〖(x^2+2x-8)/(x^2-x-2)= lim┬(x→2)⁡〖((x^2+2x-8)´)/((x^2-x-2)´)〗 〗
=lim┬(x→2)⁡〖(2x+2)/(2x-1)=(2(2)+2)/(2(2)-1)=(4+2)/(4-1)=6/3〗
=2

9.
e^x-e^y=x+y
e^x-e^y dy/dx=x+dy/dx
e^x-x=dy/dx+ey dy/dx
=dy/dx (1+e^y )
dy/dx=(e^x-x)/(1+ey)

10.
C_T (X)=100.000.000/x^2 +2x+100

〖C´〗_T (X)=100.000.000 (-2/x^3 )+2
Igualando a cero se tiene
〖C´〗_T (X)=0
100.000.000(-2/x^3)+2=0
100.000.000(2/x^3 )=2
100.000.000(1/x^3 )=1
x^3=100.000.000=x=∛100.000.000
x=464,1588834
La cantidad de bultos a solicitar para que el costo sea mínimo es 464,1588834

b) si pido más o menos valor del encontrado anteriormente, el costo aumenta. Demostremos lo anterior.
Para ellos utilizaremos el criterio de la segunda derivada, esto es si f´´ es positiva f tiene un mínimo en C ,...