Diferencial

8.- f(x)= 5x = Lim 5x
x 2 x-3 x 2 x-3

=Lim 5(2) = 10 = -10
x 2 2-3 1

LIMITES
1) lim x²-4 / x-2=0²-4 / 0-2 =4/2=2 x → 0
2) lim (x+3)(x+5) = x → 0 (1+3)(1+5)=24
3) lim 5+3/x =5+3/0=5 x = 00
4) lim x²+x = 2² + 2 = x → 2

1) 3dx / 3√x2 =3∫dx / x ⅔ =3[-⅔+3/3 / -⅔+3/3] 3[x ⅓ /⅓] = x 3/1 / ⅓ x ⅓ =9/1x⅓=9√x+c

2) ∫dx / 4x-⅓ =1/4 ∫dx / x-⅓ = 1/4∫x⅓ dx = ⅓dx =1/4 ⅓ dx =1/4[⅓+3/3/ ⅓ +3/3]=1/4[x4/3 /
3) 4/3] =3/16 – x 4/3 = 3√x4/16




4) ∫5x - ⅓dx = 5 =∫ x -⅓dx5 ∫x-⅓ + 3/3 / -⅓+3/3 =5 [ x2/2 / 2/3] = 5/1 / 2/3 [x2/3] = 15/2 x⅔ =15³√x²/2

5) ∫5 (5x+4)4ª + c ∫ (5x+4)³ 5dx = ∫v³ dv = v4ª/4 + c =(15x + 4)4ª / 4 + c

6) ∫ 3 (3x-2)² dx = ∫(3x-2)² 3dx = ∫ v² dv = v³ + c / 3 =(3x – 2 / 3)³ + c

7) ∫2 (x² - 1)² dx = ∫ (x² - 1)² 2x = ∫ x² dx = x³ / 3 + c =(x²- 1 / 3)² + c

8)

9) ∫6 x² (2x³ + 4)³ dx = ∫ ( 2x³ + 4)³6x² = ∫ x³dx = x4ª / 4 + c =(x² - 1 / 3)² + c

10) ∫(2x + 3) (x² + 3x)² dx = ∫ (2x + 3) (x² +3x)² = ∫ x²dx = x² + c =(2x + 3 / 3) (x² + 3x / 3)² + c

11) ∫(sen 2x + cos 2x) dx = ½ ∫ sen 2x+cos 2x (2) dx = ½ sen 2x – cos4x + c = √ =2x dv = 2

12) ∫x cos² x² dx = ½ ∫ x cos² x + 2x dx = ½ c/s (x²) + c = √ = x² dv = 2x

13)

15.-






6.- Y= X+2X-2
Dx = (x+2) = (1) (x+2)-(x-2)(1)
(x-2) (x-2)2

=x-2-x-2 = -4
(x-2)2 2x-4Y’= -4
2x-4

7.- y= (x+1) (x+2)
Dx= (x+1) (x+2) = (1(x+1)+(x+2)1
=x+1+x+2
Y’=2x+3






1)∫x³ cx4ª dx = 2/4 x³ ∫ x³cx³ =¼ = ¼ x³ c x4 + c √=x4 dv = 4x²

2) ∫ 3x dx / 5x² √ x4 -1 = 1/16 ∫ ½ ars sec 5x² / 1 10x = 1/10 3 ars sec 5x = 3/10ars x2 + c n=1 dv=10x v = 5x2

3) ∫6x...