Tarea De Administracion

Limites Directos.
F(x)=

1.- f(x) =2x+4
x→4
lim f(x) =2(4)+4
8+4=12
2. - f(x) =5x+10
x→2
lim f(x) =5(2)+10
10+10=20
3. - f(x) =x3
x→2
lim f(x) =23=8

4. -f(x) = x2 +12
x→0
lim f(x) = 02 +12= 12
5. - f(x) =x4+1
x→2
lim f(x)=24+1
16+1=17
Derivadas de un exponente
f(x) =xn f`(x)= nxn-1
1. - f(x) = 15x2
f`(x)= (2) (15)x2-1f`(x)= 30x

2. - f(x) =6x2
f`(x)= 12x

3. - f(x) = 120x1/2
f`(x)= (1/2) (120)x12-1
f`(x)= 60x-1/2

4. - f(x) = 6 x3/2
f`(x)= (3/2) (6)x32-1
f`(x)= 9x1/2

5. - f(x) =7x3
f`(x)=18x3Limites Indeterminados.

1.- Lim x2 -9x-3
x→3
x+3(x-3)3-3
3+3(3-3)3-3 = 6
2.- Lim x2 -1x-1
x→1
x+1(x-1)x-1
1+1(1-1)1-1 = 2
3.- Lim 4(x2 -4)x-2
x→2
4x+2(x-2)x-2
42+2(2-2)2-2 =4(4)= 164.- Lim x2 -16x-4
x→4
x+4(x-4)x-4
4+4(4-4)4-4= 8
5.- Lim x2 -4x-2
x→-2
x-2(x+2)x+2
-2-2(-2+2)-2+2 = -2-2= -4

Limites Infinitos.
1xn =0
lim
x→∞
1.- lim 3x2+2x3+x
x→∞Derivadas de Suma
F(x) ±= g(x)
F(x) ±=g'(x)
1.-f(x) =6x4+3x7+2x4-x
f'(x)= 24x3+21x6+8x3-1

2. - f(x) =6x2+x+7x1/2
f'(x)=12x+1+7/2x-1/2

3. - f(x) =3x3+2x1/2
f'(x)=9x2+x1/2

4. - f(x)=x4-6x2+6
f'(x)=4x3-12x

5. - f(x) =x6+7+x6+120x2
f'(x)=6x5+6x5+120x

Derivadas de Multiplicación.
F(x) g(x) = f(x) g´(x) g(x) f´(x).
1.-f(x) = (6x3-7) (2x2+7)
f´(x)= (6x3-7) (4x) + (2x2+7) (18x2)f´(x)=24x4-28x+36x4+126x2
f´(x)=60 x4+126x2-28x
2.- f(x) = (3x-2) (6x4+6)
f´(x)= (3x-2) (24x3)+ (6x4+6) (3)
f´(x)=72x4-48x3+18x4+18
f´(x)=90x4-48x3+18
3. - f(x) =(6x3)(x+6)
f(x) = (6x3)(x1/2+6)
f´(x)= (6x3) (12x1/2) +) (x1/2+6) (18x2)
f´(x)=3x-3/2+18x+108x2
f´(x)= 108x2+18x+3x-3/2
4. - (2x+3) (3x2+2x)
f´(x)= (2x+3) (6x+2) +) (3x2+2x) (2)f´(x)=12x2+18x+4x+6+6x2+4x
f´(x)=18x2+26x+6
5.-(x3) (3x4)
f´(x)= ( x3)(12x3) + (3x4) (3x2)
f´(x)=12x6+9x6

Derivates con división.
1. - f(x) =6x3+22x+4
ddx= 2x+418x2) –6x3+2(2)14x2+16x+16
ddx=...