Nilai dari limit x menuju tak terhingga akar x kuadrat kurang 4 x tambah 3 kurang x tambah 1

Kelas: 11
Mapel: Matematika
Kategori: Limit
Kata kunci: limit tak hingga
Kode: 11.2.7 (Kelas 11 Matematika Bab 7-Limit)

Cara Pertama:
 [tex] \lim_{x \to \infty} \sqrt{x^2-4x+3}-(x+1) \\ = \lim_{x \to \infty} \sqrt{x^2-4x+3}-(x+1)\times \frac{ \sqrt{x^2-4x+3}+(x+1) }{\sqrt{x^2-4x+3}+(x+1)} \\ = \lim_{x \to \infty} \frac{x^2-4x+3-(x+1)^2}{\sqrt{x^2-4x+3}+(x+1)} \\ = \lim_{x \to \infty} \frac{x^2-4x+3-(x^2+2x+1) }{\sqrt{x^2-4x+3}+(x+1)} \\ = \lim_{x \to \infty} \frac{-6x+2}{\sqrt{x^2-4x+3}+(x+1)}[/tex]
[tex]= \lim_{x \to \infty} \frac{ \frac{-6x}{x} + \frac{2}{x} }{\sqrt{ \frac{x^2}{x^2} - \frac{4x}{x^2} + \frac{3}{x^2} }+( \frac{x}{x} + \frac{1}{x} )} \\ = \frac{-6+0}{ \sqrt{1+0+0)}+(1+0) } \\ =- \frac{6}{2} \\ =-3 [/tex]

Cara kedua:
[tex] \lim_{x \to \infty} \sqrt{ax^2+bx+c}- \sqrt{ax^2+px+q}= \frac{b-p}{2 \sqrt{a} } \\ \\ \lim_{x \to \infty} \sqrt{x^2-4x+3}-(x+1) \\ = \lim_{x \to \infty} \sqrt{x^2-4x+3}- \sqrt{(x+1)^2 } \\ = \lim_{x \to \infty} \sqrt{x^2-4x+3}- \sqrt{x^2+2x+1 } \\ = \frac{-4-2}{2 \sqrt{1} } \\ = \frac{-6}{2} \\ =-3 [/tex]

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Semoga membantu :)