Question

Lim x-√x / 1-x² = …
x→ 1

Answer 1

Lim(x→1) (x-√x) / (1-x²)
= lim(x→1) √x(√x-1) / (1-x)(1+x)  
= lim(x→1) √x(√x-1) / (1-√x)(1+√x)(1+x)     
= lim(x→1) -√x(1-√x) / (1-√x)(1+√x)(1+x)      ; coret (1-√x)
= lim(x→1) -√x / (1+√x)(1+x)                         ; subtitusi x =1
= -√1 / (1+√1)(1+1) 
= -1 / (2)(2)
= -1/4