Question

Lim = x^5-1\x^3-1 помогите алгебра
x=>1

Answer 1

Неопределенность  типа 0/0.
Lim→1 (x⁵ -1)/(x³-1) =Lim→1 (x-1)(x⁴ +x³ +x² +x +1)/(x-1)(x² +x+1) =
Lim→1 (x⁴ +x³ +x² +x +1)/(x² +x+1) =5/3.

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(x⁵-1)/(x³-1) =(x⁵ -x² +x²-1)/(x³ -1) = (x⁵ -x²)//(x³ -1) +(x²-1)/x³ -1)  =
x²(x³ -1 )/(x³ -1)  +(x-1)(x+1)/(x-1)(x²+x+1)= x² +(x+1)/(x²+x+1).
Lim→1 (x⁵-1)/(x³-1) =Lim→1  ( x² +(x+1)/(x²+x+1) ) =1²+(1+1)/(1².+1+1) =1+2/3 =5/3.

Answer 2

Lim(x² + (x²-1)/(x³-1))=lim(x² +(x-1)(x+1)/(x-1)(x²+x=1))=lim(x²+(x+1)/(x²+x+1))=
=1+2/3=1 2/3