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Jawaban:
Nilai dari [tex] \tt lim_{x\: \to \: 5} \: \frac{(x - 5)}{6 - \sqrt{x^{2} + 11}} [/tex] adalah [tex] \sf -\frac{6}{5} [/tex].
Pembahasan
[tex] \tt lim_{x\: \to \: 5} \: \frac{(x - 5)}{6 - \sqrt{x^{2} + 11}} [/tex]
[tex] \tt lim_{x\: \to \: 5} \: \frac{(x - 5)}{6 - \sqrt{x^{2} + 11}} \:x\: \frac{6 + \sqrt{x^{2} + 11}}{6 + \sqrt{x^{2} + 11}} [/tex]
[tex] \tt lim_{x\: \to \: 5} \: \frac{(x - 5)(6 + \sqrt{x^{2} + 11)}}{ (6^{2}) - (\sqrt{x^{2}+ 11)^{2}}} [/tex]
[tex] \tt lim_{x\: \to \: 5} \: \frac{(x - 5)(6 + \sqrt{x^{2} + 11)}}{36 - (x^{2} + 11)} [/tex]
[tex] \tt lim_{x \: \to \: 5} \: \frac{(x - 5)(6 + \sqrt{x^{2} + 11)}}{36 - x^{2} - 11} [/tex]
[tex] \tt lim_{x \: \to \: 5} \: \frac{(x - 5)(6 + \sqrt{x^{2} + 11)}}{-x^{2} + 25} [/tex]
[tex] \tt lim_{x \: \to \: 5} \: \frac{(x - 5)(6 + \sqrt{x^{2} + 11)}}{(5 + x)(5 - x)} [/tex]
[tex] \tt lim_{x \: \to \: 5} \: \frac{-\cancel{(5 - x)}(6 + \sqrt{x^{2} + 11)}}{(5 + x)\cancel{(5 - x)}} [/tex]
[tex] \tt lim_{x \: \to \: 5} \: \frac{-(6 + \sqrt{x^{2} + 11)}}{(5 + x)} [/tex]
Substitusi nilai x = 5.
= [tex] \tt \frac{-(6 + \sqrt{x^{2} + 11)}}{(5 + x)} [/tex]
= [tex] \tt \frac{-(6 + \sqrt{5^{2} + 11)}}{(5 + 5)} [/tex]
= [tex] \tt \frac{-(6 + \sqrt{(25 + 11)}}{10} [/tex]
= [tex] \tt \frac{-(6 + \sqrt{36})}{10} [/tex]
= [tex] \tt \frac{-(6 + 6)}{10} [/tex]
= [tex] \tt -\frac{12}{10} \: \approx \: -\frac{6}{5} [/tex]
Kesimpulan
Berdasarkan perhitungan diatas bahwa nilai dari [tex] \tt lim_{x\: \to \: 5} \: \frac{(x - 5)}{6 - \sqrt{x^{2} + 11}} [/tex] tersebut adalah [tex] \sf -\frac{6}{5} [/tex].
Pelajari Lebih Lanjut
1. Limit tak hingga fungsi rasional: https://brainly.co.id/tugas/30037968
2. Limit tak hingga fungsi rasional: https://brainly.co.id/tugas/28942347
3. Limit tak hingga bentuk akar: https://brainly.co.id/tugas/32409886
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Detail Jawaban
Kelas : 11
Mapel : Matematika
Bab : Limit Fungsi Aljabar
Kode Kategorisasi : 11.2.8
Kata Kunci : limit, fungsi, rasional
Penjelasan dengan langkah-langkah:
jawaban:
C.
semoga membantuu.
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