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Leonardo2424
@Leonardo2424
August 2019
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Calcule e justifique:
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(x+1)³=x³+3x²+3x+1
(x+1)³=x³+1+3x*(x+1)
x³+1 =(x+1)³-3x*(x+1)
x³+1=(x+1)*[(x+1)²-3x]
x³+1=(x+1)*[x²+2x+1-3x]
x³+1=(x+1)*(x²+1-x)
x²-1=(x+1)*(x-1)
##################################
Lim (x+1)*(x²+1-x)/(x+1)*(x-1)
x-->-1
Lim (x+1)*(x²+1-x)/(x+1)*(x-1)
x-->-1
Lim (x²+1-x)/(x-1) =(1+1+1)/(-2) =-3/2
x-->-1
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(x+1)³=x³+1+3x*(x+1)
x³+1 =(x+1)³-3x*(x+1)
x³+1=(x+1)*[(x+1)²-3x]
x³+1=(x+1)*[x²+2x+1-3x]
x³+1=(x+1)*(x²+1-x)
x²-1=(x+1)*(x-1)
##################################
Lim (x+1)*(x²+1-x)/(x+1)*(x-1)
x-->-1
Lim (x+1)*(x²+1-x)/(x+1)*(x-1)
x-->-1
Lim (x²+1-x)/(x-1) =(1+1+1)/(-2) =-3/2
x-->-1