Question

Tentukan nilai dari limit berikut!
[tex]\displaystyle\lim_{x \to \infty} \sqrt{{x}^{2} + x - 2} - x - 2[/tex]
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Selamat Berjuang​

Answer 1

Verified answer

Jawab:

[tex]\lim_{x \to \infty} \sqrt{x^{2} +x-2} -x-2\\\\ = \lim_{x \to \infty} (\sqrt{x^{2} +x-2}-x)- \lim_{x \to \infty} 2 \\\\= \frac{1}{2}- 2\\\\=-\frac{3}{2}[/tex]

Answer 2

∞ Limit Tak Hingga ∞

[tex]\sf \lim\limits_{x \to \infty} \sqrt{x^{2} +x-2}-x-2\\\\=\lim\limits_{x \to \infty} \sqrt{x^{2} +x-2}-(x+2)\\\\=\lim\limits_{x \to \infty} (\sqrt{x^{2} +x-2}-\sqrt{(x+2)^{2}} \\\\=\lim\limits_{x \to \infty} (\sqrt{x^{2} +x-2}-\sqrt{x^{2}+4x+4}[/tex]

Jika bentuk  [tex]\sf \lim\limits_{x \to \infty} (\sqrt{ax^{2}+bx+c } -\sqrt{px^{2} +qx+r} )[/tex]  dengan a = p

Maka hasilnya [tex]\sf \frac{b-q}{2\sqrt{a} }[/tex] .

[tex]\sf\\=\frac{1-4}{2\sqrt{1} }\\\\=\frac{-3}{2\cdot 1} \\\\\boxed{\sf =-\frac{3}{2} }[/tex]

Jadi, hasil limit tak hingga tersebut adalah -3/2.

[tex]\boxed{\sf{shf}}[/tex]