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Y=3 x2+4
1.paso
y+∆y=3x+∆x2+4
Y+∆y=3〔x2+2x∆x+∆x〕2+4
Y+∆y=3x2+6x∆x+3∆x2+4
2.paso
Y+∆y=3x2+6x∆x+3∆x2+4-y+ =3x2 -4
∆y= 6x∆x+3∆x2
3.paso
∆y∆x=6x∆x+3∆x2∆x ∆x
∆y∆x=6x+3∆x
4.paso
lim∆y∆x=6x+3∆x
=6x+3(0)
=6x
1.pasoy=3x
y+∆y=3x+∆x
2.paso
Y+∆y=3(x+∆x
-y+ =-3x__________
∆y= 3∆x
3.paso
∆y∆x= 3∆x∆x
∆y∆x=3
4.paso
lim∆y∆x=3ddx(3x)=3
1.paso
y=x3-x+2
y+∆y=x+∆x3-x+∆x+2
Y+∆y=〔x3+3x2∆x+3x∆x2+∆x3-x+∆x+2
Y+∆y=
2.paso
Y+∆y=〔x3+3x2∆x+3x∆x2+∆x3-x+∆x+2
-y+ =-x3+x -2
∆y= 3x2∆x+3∆x2+∆x3-∆x
3.paso
∆y∆x= 3x2∆x+ 3∆x2+ ∆x3-∆x∆x ∆x ∆x
∆y∆x=3x2+3∆x+∆x2
4.pasolim∆y∆x=3x2+3∆x+∆x2
=3x2+3∆x(0) (0)
=3x2
1.paso
Y=1x
2.paso
Y+∆y=1-1
-y x+∆x-x
∆y=x-(x+∆x)x+x∆x=x-x-∆x x2+x∆x=-∆x x2+x∆x
3.paso
∆y∆x=-∆xx2+x∆x∆x
1
-∆x∆x(x2+x∆x)
4.paso
lim∆y∆x=-1x2+x∆x=-1x2+x(0)
=-1x2+
1.paso
Y=5x3
Y+ ∆y=5(x+∆x)3=5x5∆x 3
2.paso
Y+ ∆y=5(x+∆x)3-5x 3=5∆x3
-y_____________________
∆y=5∆x3
3.paso
∆y∆x=5∆x3 ∆x
1
∆y∆x=5∆x3∆x
4.paso
lim∆y∆x=53
1.paso y=-x
y+∆y=-1x+∆x
2.paso
Y+∆y=-x+∆x
-y+ =x__________
∆y= ∆x
3.paso
∆y∆x= ∆x∆x
∆y∆x=1
4.paso
lim∆y∆x=1
1.paso
Y=-3x2
Y+ ∆y=-32(x+∆x)
2.paso
Y+ ∆y=-3x2-3∆x2-3x2
-y _____________________
∆y=-3∆x2
3.paso
∆y∆x=-3∆x2 ∆x
1
∆y∆x=3∆x2∆x
∆y∆x=-32
4.paso
lim∆y∆x=-32
1.paso
Y+∆y=3x+2...
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