nilai dari limit 1+2x / 2-√6+4x adalah x-> 1/2

Bab Limit
Matematika SMA Kelas XI

karena bentuknya bukan 0/0, maka

lim ((1 + 2x) / (2 - √(6 + 4x))
x→1/2 
= (1 + 2 . 1/2) / (2 - √(6 + 4 . 1/2))
= (1 + 1) / (2 - √(6 + 2))
= 2 / (2 - √8)
= 2 / (2 - 2√2)
= 1/(1 - √2)
= (1 + √2) / (1² - √2²)
= (1 + √2) / (1 - 2)
= (1 + √2) / -1
= -1 - √2

[tex]\displaystyle \lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}\cdot\frac{2+\sqrt{6+4x}}{2+\sqrt{6+4x}}\\\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\lim_{x\to-\frac12}\frac{(1+2x)(2+\sqrt{6+4x})}{4-6-4x}\\\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\lim_{x\to-\frac12}\frac{(1+2x)(2+\sqrt{6+4x})}{-2-4x}\\\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\lim_{x\to-\frac12}\frac{(1+2x)(2+\sqrt{6+4x})}{-2(1+2x)}[/tex]
[tex]\displaystyle \lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\lim_{x\to-\frac12}\frac{2+\sqrt{6+4x}}{-2}\\\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\frac{2+\sqrt{6-4\cdot\frac12}}{-2}\\\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\frac{2+\sqrt{4}}{-2}\\\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=\frac{2+2}{-2}\\\boxed{\boxed{\lim_{x\to-\frac12}\frac{1+2x}{2-\sqrt{6+4x}}=-2}}[/tex]