Question

LIMIT AKAR tolong bantuannya kak soal Limit Akar

lim
x->4
[tex] \frac{x - 4}{ \sqrt{x {}^{2} - 16 } } = [/tex]

tolong Jawab menggunakan metode rasionalisasi penyebut atau Rumus L Hopital limit akar


tolong bantuan nya terima kasih kak semoga menjadi berkah ilmunya amal jariyah​

Answer 1

Verified answer

limit fungsi rasional

-

Rasionalisasi Penyebut.

[tex]\rm{\lim\limits_{x \to 4} \frac{x - 4}{\sqrt{x^{2} - 16}}}[/tex]

[tex]\rm{\lim\limits_{x \to 4} \frac{x - 4}{\sqrt{x^{2} - 16}} \times \frac{\sqrt{x^{2} - 16}}{\sqrt{x^{2} - 16}}}[/tex]

[tex]\rm{\lim\limits_{x \to 4} \frac{(4 - x)(\sqrt{x^{2} - 16})}{x^{2} - 16}}[/tex]

[tex]\rm{\lim\limits_{x \to 4} \frac{-\cancel{(x - 4)}(\sqrt{x^{2} - 16})}{\cancel{(x - 4)}(x + 4)}}[/tex]

[tex]\rm{L = -\frac{\sqrt{16 - 16}}{4 + 4}}[/tex]

[tex]\rm{L = 0}[/tex]

L'Hopital

[tex]\boxed{\rm{\lim\limits_{x \to a} \frac{f(x)}{g(x)} \leftrightarrow L = \frac{f'(a)}{g'(a)}}}[/tex]

maka,

[tex]\rm{\lim\limits_{x \to 4} \frac{x - 4}{\sqrt{x^{2} - 16}}}[/tex]

[tex]\rm{\lim\limits_{x \to 4} \: \frac{1}{\frac{1}{2} (x^{2} - 16)^{-\frac{1}{2}} . 2x}}[/tex]

[tex]\rm{\lim\limits_{x \to 4} \: \sqrt{x^{2} - 16}}[/tex]

[tex]\rm{L = \sqrt{4^2 - 16}}[/tex]

[tex]\rm{L = 0}[/tex]

_____