[tex] \frac{ \sqrt{3 + x} - \sqrt{2x} }{3 - x} [/tex]
dengan x mendekati 3
Nilai dari [tex]\displaystyle{ \lim_{x \to 3} \frac{\sqrt{3+x}-\sqrt{2x}}{3-x} }[/tex] adalah [tex]\displaystyle{\boldsymbol{\frac{1}{12}\sqrt{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 3} \frac{\sqrt{3+x}-\sqrt{2x}}{3-x}= }[/tex]
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DITANYA
Tentukan nilai limitnya.
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PENYELESAIAN
Kita kalikan dengan akar sekawannya.
[tex]\displaystyle{ \lim_{x \to 3} \frac{\sqrt{3+x}-\sqrt{2x}}{3-x} }[/tex]
[tex]\displaystyle{=\lim_{x \to 3} \frac{\sqrt{3+x}-\sqrt{2x}}{3-x}\times\frac{\sqrt{3+x}+\sqrt{2x}}{\sqrt{3+x}+\sqrt{2x}} }[/tex]
[tex]\displaystyle{=\lim_{x \to 3} \frac{3+x-2x}{(3-x)(\sqrt{3+x}+\sqrt{2x})} }[/tex]
[tex]\displaystyle{=\lim_{x \to 3} \frac{\cancel{(3-x)}}{\cancel{(3-x)}(\sqrt{3+x}+\sqrt{2x})} }[/tex]
[tex]\displaystyle{=\lim_{x \to 3} \frac{1}{\sqrt{3+x}+\sqrt{2x}} }[/tex]
[tex]\displaystyle{=\frac{1}{\sqrt{3+3}+\sqrt{2(3)}} }[/tex]
[tex]\displaystyle{=\frac{1}{2\sqrt{6}}\times\frac{\sqrt{6}}{\sqrt{6}} }[/tex]
[tex]\displaystyle{=\frac{1}{12}\sqrt{6} }[/tex]
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KESIMPULAN
Nilai dari [tex]\displaystyle{ \lim_{x \to 3} \frac{\sqrt{3+x}-\sqrt{2x}}{3-x} }[/tex] adalah [tex]\displaystyle{\boldsymbol{\frac{1}{12}\sqrt{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.
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