Nilai dari [tex]\displaystyle{ \lim_{x \to -2} \frac{\sqrt{2x+13}-\sqrt{x+11}}{x+2} }[/tex] adalah [tex]\displaystyle{\boldsymbol{\frac{1}{6}} }[/tex].
PEMBAHASAN
Teorema pada limit adalah sebagai berikut :
[tex](i)~\lim\limits_{x \to c} f(x)=f(c)[/tex]
[tex](ii)~\lim\limits_{x \to c} kf(x)=k\lim\limits_{x \to c} f(x)[/tex]
[tex](iii)~\lim\limits_{x \to c} [f(x)\pm g(x)]=\lim\limits_{x \to c} f(x)\pm\lim\limits_{x \to c} g(x)[/tex]
[tex](iv)~\lim\limits_{x \to c} [f(x)\times g(x)]=\lim\limits_{x \to c} f(x)\times\lim\limits_{x \to c} g(x)[/tex]
[tex](v)~\lim\limits_{x \to c} \left [ \frac{f(x)}{g(x)} \right ]=\frac{\lim\limits_{x \to c} f(x)}{\lim\limits_{x \to c} g(x)}[/tex]
[tex](vi)~\lim\limits_{x \to c} \left [ f(x) \right ]^n=\left [ \lim\limits_{x \to c} f(x) \right ]^n[/tex]
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DIKETAHUI
[tex]\displaystyle{ \lim_{x \to -2} \frac{\sqrt{2x+13}-\sqrt{x+11}}{x+2}= }[/tex]
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DITANYA
Tentukan nilai limitnya.
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PENYELESAIAN
Kita kalikan dengan akar sekawannya.
[tex]\displaystyle{ \lim_{x \to -2} \frac{\sqrt{2x+13}-\sqrt{x+11}}{x+2} }[/tex]
[tex]\displaystyle{= \lim_{x \to -2} \frac{\sqrt{2x+13}-\sqrt{x+11}}{x+2}\times\frac{\sqrt{2x+13}+\sqrt{x+11}}{\sqrt{2x+13}+\sqrt{x+11}} }[/tex]
[tex]\displaystyle{= \lim_{x \to -2} \frac{2x+13-x-11}{(x+2)(\sqrt{2x+13}+\sqrt{x+11})} }[/tex]
[tex]\displaystyle{= \lim_{x \to -2} \frac{\cancel{(x+2)}}{\cancel{(x+2)}(\sqrt{2x+13}+\sqrt{x+11})} }[/tex]
[tex]\displaystyle{= \lim_{x \to -2} \frac{1}{\sqrt{2x+13}+\sqrt{x+11}} }[/tex]
[tex]\displaystyle{=\frac{1}{\sqrt{2(-2)+13}+\sqrt{(-2)+11}} }[/tex]
[tex]\displaystyle{=\frac{1}{\sqrt{9}+\sqrt{9}} }[/tex]
[tex]\displaystyle{=\frac{1}{6} }[/tex]
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KESIMPULAN
Nilai dari [tex]\displaystyle{ \lim_{x \to -2} \frac{\sqrt{2x+13}-\sqrt{x+11}}{x+2} }[/tex] adalah [tex]\displaystyle{\boldsymbol{\frac{1}{6}} }[/tex].
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PELAJARI LEBIH LANJUT
- Limit fungsi : https://brainly.co.id/tugas/30319110
- Limit tak hingga : https://brainly.co.id/tugas/28942347
- Limit fungsi trigonometri : https://brainly.co.id/tugas/30308496
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DETAIL JAWABAN
Kelas : 11
Mapel: Matematika
Bab : Limit Fungsi
Kode Kategorisasi: 11.2.8
Kata Kunci : limit, fungsi, akar, sekawan.
