Lim x Mendekati 2 √3x-√6/2-x
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Penjelasan dengan langkah-langkah:
[tex]\lim_{x \to \ 2} \frac{\sqrt{3x}-\sqrt{6} }{2-x} = \frac{\sqrt{3(2)}-\sqrt{6} }{2-2} =\frac{\sqrt{6}-\sqrt{6} }{2-2} = \frac{0}{0}[/tex]
Didapatkan hasil 0/0, maka harus menggunakan cara yang lain.
Dengan perkalian sekawan :
[tex]\lim_{x \to \ 2} \frac{\sqrt{3x}-\sqrt{6} }{2-x} = \lim_{x \to \ 2} \frac{\sqrt{3x}-\sqrt{6} }{2-x} (\frac{\sqrt{3x}+\sqrt{6} }{\sqrt{3x}+\sqrt{6}}) = \lim_{x \to \ 2} \frac{3x-6 }{(2-x)(\sqrt{3x}+\sqrt{6})}\\ = \lim_{x \to \ 2} \frac{3(x-2) }{-(x-2)(\sqrt{3x}+\sqrt{6})} =\lim_{x \to \ 2} \frac{3 }{-(\sqrt{3x}+\sqrt{6})} = \frac{3}{-(\sqrt{6}+\sqrt{6}) } = -\frac{3}{2\sqrt{6} } \\= - \frac{3\sqrt{6} }{12 } = - \frac{\sqrt{6} }{4}[/tex]
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