Limit 2X ________ X=>0 2-√4-4X

Bab Limit
Matematika SMA Kelas XI

lim (2x / (2 - √(4 - 4x)))
x→0

= lim (2x . (2 + √(4 - 4x))/(2² - √(4 - 4x)²))
   x→0

= lim (2x . (2 + √(4 - 4x)) / (4 - 4 + 4x))
  x→0

= lim (2x . (2 + √(4 - 4x)) / 4x)
   x→0

= (2 + √(4 - 0)) / 2
= (2 + 2)/2
= 2

[tex]\displaystyle \lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}=\lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}\cdot\frac{2+\sqrt{4-4x}}{2+\sqrt{4-4x}}\\\lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}=\lim_{x\to0}\frac{2x(2+\sqrt{4-4x})}{4-4+4x}\\\lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}=\lim_{x\to0}\frac{2x(2+\sqrt{4-4x})}{4x}\\\lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}=\lim_{x\to0}\frac{2+2\sqrt{1-x}}{2}\\\lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}=\lim_{x\to0}1+\sqrt{1-x}\\\lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}=1+1\sqrt{1-0}[/tex]
[tex]\displaystyle \boxed{\boxed{\lim_{x\to0}\frac{2x}{2-\sqrt{4-4x}}=2}}[/tex]