Hitunglah setiap limit yang di berikan Lim x tanda panah 2 , tan akar 6-x-2, per x-2

[tex]\displaystyle \lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=\lim_{x\to2}\frac{\tan(\sqrt{6-x}-2\cdot\frac{\sqrt{6-x}+2}{\sqrt{6-x}+2})}{x-2}\\\lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=\lim_{x\to2}\frac{\tan\left(\frac{6-x-4}{\sqrt{6-x}+2}\right)}{x-2}\\\lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=\lim_{x\to2}\frac{\tan\left(\frac{2-x}{\sqrt{6-x}+2}\right)}{x-2}\\\lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=\lim_{x\to2}\frac{\tan\left(-\frac{x-2}{\sqrt{6-x}+2}\right)}{x-2}[/tex]
[tex]\displaystyle \lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=\lim_{x\to2}\frac{-\tan\left[(x-2)\left(\frac{1}{\sqrt{6-x}+2}\right)\right]}{x-2}\\\lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=\lim_{x\to2}-\frac{1}{\sqrt{6-x}+2}\\\lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=-\frac{1}{\sqrt{6-2}+2}\\\boxed{\boxed{\lim_{x\to2}\frac{\tan(\sqrt{6-x}-2)}{x-2}=-\frac{1}{4}}}[/tex]

Lim Tan (√(6 - x) - 2) / (x - 2)
x=>2

Lim Tan (√(6 - x) - 2)/(x - 2) . (√(6 - x) - 2)/(√(6 - x) - 2)
x=>2

Lim (Tan (√(6 - x) - 2))/(√(6 - x) - 2) . (√(6 - x) - 2)/(x - 2)
x=>2

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

Lim ((6 - x) - 4) / (x - 2)(√(6 - x) + 2)
x=>2

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

Lim 1 / -(√(6 - x) + 2)
x=>2

= 1 / -(√(6 - 2) + 2)

= -1 / (√4 + 2)

= -1/4