Question

Alguem pode me ajudar?
lim (x^4 -1)/(x^3 -1) com x tendendo a 1

Answer 1

lim (x^4 -1)/(x^3 -1) 
x-->1

****x^4-1 =(x²-1)*(x²+1) =(x-1)(x+1)*(x²+1)

****(x-1)³=x³-3x²+3x-1
****(x-1)³=x³-1 -3x²+3x
****(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)


lim (x^4 -1)/(x^3 -1) 
x-->1

lim (x-1)(x+1)*(x²+1)/(x-1)*(x²+1+x)
x-->1

lim (x+1)*(x²+1)/(x²+1+x) =(1+1)*(1+1)/(1+1+1) =4/3
x-->1