Practica Calculo

20-FEBRERO-2013
PRACTICA 1·
1. Si f es una función cuyo dominio es el conjunto de los números reales y con regla de correspondencia hallar:
f (x) = 3x2 –2x + 5 HALLAR:
a) f (2)
b) f (-2/3)
c) f (x+h)
1. f (x) = 3x2 – 2x + 5
f (2)
f (x) = 3x2 – 2x + 5
f (2)= 3 (2)2 – 2 (2) + 5
f (2) = 12 – 4 + 5
f (2) = 17 – 4
f (2) = 13

2. f (x) = 3x2 – 2x + 5
f (-2/3)
f -23=3 -23- 2 -23+5
f-23= 3 49+43+5
f -23=129+43+5
f -23=83+51+233
129+43=12+129=249=83
f -23=233

3. f x= 3x2-2x+5
f x+h
f x+h= 3 x+h2-2 x+h+ 5
f x+h= 3 x2+2xh+h2- 2x+h+5
f x+h= 3x2+6xh+3h2-2x-2h+5

25-FEBRERO-2013
PRACTICA 2·
Realizar los ejercicios
1.
limh→∞ax2+bx2+c dx5+ex3+fx =∞limh→∞ax4x5+bx2x5+cx5=ax+bx3+cx5dx5x5+ex3x5+fxx5=a+ex2+fx4
a∞+b∞+c∞
d+e∞2+f∞4

2.
limx→∞ax4+bx2+c dx3+cx2+fx+g =∞
ax4x4+bx2x4+cx4
dx3x4+cx2x4+fxx4+gx4
3.
lims→as4s2-a4a2=2a2
lims→as2+as2-a2s2-a2 =s2+a2=a2+a2=2a2

4.
limx→2x2+x-6x2-4 =54
limx→2x+3x-2=x+3=2+3x+2x-2 x+2=2+2 =54
5.
Dado f x= ax3
limh→0fx+h-fxh =3ax3
fx=ax3
fx+h=a x+h3
fx+h= a(x3+x2h+3xh2+h3)
fx+h= a fx+x3h+3xh2+h3
fx+h-fxh = a+3x2h+3xh2+h3h
fx+h-fxh =a+3x2+3xh+h
limh→0fx+h-fxh =a+3x2+3xh+h2
fx+h-fxh=a+3x2+3x0+02
fx+h-fxh =a+3x2=3ax2
6.
Dado fx= x2-3x+5 HALLAR
limh→0fx+h-fxh =2x-3
fx= x2-3x+5
fx+h=x+h2-3 x+h+5
fx+h=x2+4xh+h2±3x-3h+5fx+h)=x2-3x+5+2xh+h2-3h
fx+h= fx+2xh+h2+3h
fx+hh = fx+2xh+h2-3hh
fx+hh-f(x) = 2xh+h2-3hh
fx+hh-fx = 2x+h-3
limh→0fx+h-fxh =2x+ (0)-3
limh→0fx+h-fxh =2x-3