Novo

Y= 4x2+3

1°- ∆
Y+∆y = 4(x+∆x)2+3
Y+∆y = 4(x2+2x∆x+ (∆x)2)+3
Y+∆y = 4x2+8x∆x+4(∆x)2+3

2°- y+∆y = 4x2+8x∆x+4(∆x)2+3
-y =-4x2 -3
∆y =8x∆x+4(∆x)2

3°- ∆y/∆x = 8x∆x+4(∆x)2
∆x
∆y/∆x = 8x+4(∆x)

4°- Lim
∆x 0
8x+4(0) = 8x
∆y/∆x = 8x

Y = 5x2+6x

1° ∆
Y+∆y = 5(x+∆x)2+6(x+∆x)
Y+∆y = 5(x2+2x∆x+∆x2)+6x+6∆xY+∆y = 5x2+10x∆x+5∆x2+6x+6∆x

2°- Y+∆y = 5x2+10x∆x+5∆x2+6x+6∆x
-y =-5x2 -6x
∆y = 10x∆x+5∆x2 +6∆x

3°- ∆y/∆x = 10x∆x+5∆x2+6∆x
∆x
∆y/∆x = 10x+5∆x+6

4°- Lim
∆x 0
∆y/∆x = 10x+5(0)+6
∆y/∆x = 10x+6

Y = 8x3+6x2+4x-5

1°- ∆
Y+∆y = 8(x+∆x)3+6(x+∆x)2+4(x+∆x)-5
Y+∆y =8(x3+3x∆x+(∆x)3)+6(x2+2x∆x+(∆x)2)+4x+4∆x-5
Y+∆y = 8x3+24x∆x+8∆x3+6x2+12x∆x+6∆x2+4x+4∆x-5

2°- -y+∆y = 8x3+24x∆x+8∆x3+6x2+12x∆x+6∆x2+4x+4∆x-5
-y = -8x3 -6x2-4x +5
∆y = 24x∆x+8∆x3 +12x∆x+6∆x2 +4∆x

3°- ∆y/∆x = 24x∆x+8∆x3+12x∆x+6∆x2+4∆x
∆x
∆y/∆x =24x+8∆x+12x+6∆x+4

4°- Lim
∆x 0
∆y/∆x = 24x+8(0)+12x+6(0)+4
∆y/∆x = 24x+12x+4

Y= 2x2
x+3
1°- ∆
Y+∆y = 2(x+∆x)2
(x+4x)+3
Y+∆y = 2(x2+2x∆x+(∆x)2)(x+∆x)+3
Y+∆y = 2x2+4x∆x+2(∆x)2
X+∆x+3

2°- y+∆y = 2x2+4x∆x+2(∆x)2
X+∆x+3
-y = -2x2
X+3
∆y =2x2+4x∆x+2(∆x)2 – 2x2
X+∆x+3 x+3
∆y = (x+3)(2x2+4x∆x+2(∆x)2)-(2x2)(x+∆x+3)
(x+3)(x+∆x+3)
3°-∆y/∆x = (2x2+4x∆x+2(∆x)2)-(2x2)
∆x
∆y/∆x= 2x+4x+2∆x-2x
4°- Lim
∆x 0
∆y/∆x = 2x+4x+2(0)-2x
∆y/∆x = 2x+4x-2...