..
[tex] \displaystyle \sf \lim_{x \to9} \: \frac{x - 9}{ \sqrt{x} - 3 } [/tex]
Selesaikan dengan aturan L'hospital
Penyelesaian
lim x → 9 (x - 9) / (√x - 3)
lim x → 9 (1 . x¹⁻¹ - 0 . 9x⁰⁻¹) / (1/2 . x^(1/2 - 2/2) - 0 . 3x⁰⁻¹)
lim x → 9 (1 - 0) / (1/2x^(-1/2) - 0)
lim x → 9 1 / ((1/2 . 1/√x) - 0)
lim x → 9 1 / (1/2√x)
1 ÷ (1/2√9)
1 × (2(3))
6
[tex]~[/tex]
Detail Jawaban
- Mapel: Matematika
- Kelas: 11 (2 SMA)
- Materi: Limit
- Kode Mapel: 2
- Kode Kategorisasi: 11.2.sekian
⟩ Limit fungsi aljabar
Aturan L'Hospital?
[tex] \sf \lim_{x \to \: a} \frac{f(x)}{g(x)} \to \lim_{x \to \: a} \frac{f'(x)}{g'(x)} [/tex]
__________
[tex]\displaystyle \sf \lim_{x \to9} \: \frac{x - 9}{ \sqrt{x} - 3 }[/tex]
[tex] \sf \lim_{x \to \: 9} \frac{ {x}^{0} - 9(0)}{ {(x)}^{ \frac{1}{2} } - 3(0)} \\ [/tex]
[tex] \sf \lim_{x \to \: 9} \frac{ {x}^{0} - 0}{ \frac{1}{2}(x) {}^{ \frac{1}{2} - 1 } - \: 0 } \\ [/tex]
[tex] \sf \lim_{x \to9} \frac{1 - 0}{ \frac{1}{2 {x}^{ \frac{1}{2} } } } \\ [/tex]
[tex] \sf \lim_{x \to \: 9} \frac{1}{ \frac{1}{2 \sqrt{x} } } \\ [/tex]
[tex] \sf \lim_{x \to \: 9}1 \div \frac{1}{2 \sqrt{x} } \\ [/tex]
[tex] \sf \lim_{x \to \: 9}1 \times \frac{2 \sqrt{x} }{1} \\ [/tex]
[tex] \sf \lim_{x \to 9}2 \sqrt{x} [/tex]
[tex] \sf \to2 \sqrt{9} [/tex]
[tex] \sf \to2 \sqrt{ {3}^{2} } [/tex]
[tex] \sf \to2(3)[/tex]
[tex] \sf \to6[/tex]
- Kesimpulan
- Jadi, hasil dari limit teresebut adalah 6
~ Riisaa
