Nilai Dari lim x mendekati 1 6x-6/1-x√x adalah

Lim (6x - 6)/(1 - x√x)
x=>1

Lim (6x - 6)/(1 - x√x) . (1 + x√x)/(1 + x√x)
x=>1

Lim (6x - 6)(1 + x√x) / (1 - x^3)
x=>1

Lim 6(x - 1)(1 + x√x) / -(x^3 - 1)
x=>1

Lim 6(x - 1)(1 + x√x) / -(x - 1)(x^2 + x + 1)
x=>1

Lim 6(1 + x√x) / -(x^2 + x + 1)
x=>1

= 6(1 + 1√1) / -(1 + 1 + 1)

= 6(2) / -3

= -4

[tex]\displaystyle \lim_{x\to1}\frac{6x-6}{1-x\sqrt x}=\lim_{x\to1}\frac{6x-6}{1-x\sqrt x}\cdot\frac{1+x\sqrt x}{1+x\sqrt x}\\\lim_{x\to1}\frac{6x-6}{1-x\sqrt x}=\lim_{x\to1}\frac{6(x-1)(1+x\sqrt x)}{(1-x^3)}\\\lim_{x\to1}\frac{6x-6}{1-x\sqrt x}=\lim_{x\to1}\frac{6(x-1)(1+x\sqrt x)}{(1-x)(1+x+x^2)}\\\lim_{x\to1}\frac{6x-6}{1-x\sqrt x}=\lim_{x\to1}\frac{-6(1+x\sqrt x)}{1+x+x^2}\\\lim_{x\to1}\frac{6x-6}{1-x\sqrt x}=\frac{-6(1+1\sqrt1)}{1+1+1^2}\\\lim_{x\to1}\frac{6x-6}{1-x\sqrt x}=\frac{-6(2)}{3}[/tex]
[tex]\displaystyle \boxed{\boxed{\lim_{x\to1}\frac{6x-6}{1-x\sqrt x}=-4}}[/tex]