Matematika

Pertanyaan

Nilai lim x=6 √2x+4-√3x-2/x-6????

1 Jawaban


  • [tex]lim = \frac{ \sqrt{2x + 4} - \sqrt{3x - 2} }{x - 6} \\ x - 6[/tex]
    [tex] = \frac{( \sqrt{2x + 4} - \sqrt{3x - 2})( \sqrt{2x + 4} + \sqrt{3x - 2} ) }{(x - 6)( \sqrt{2x - 4} + \sqrt{3x - 2} )} [/tex]
    [tex] = \frac{ -x + 6}{(x - 6)( \sqrt{2x + 4 4} + \sqrt{3x - 2} ) } [/tex]

    [tex] = - \frac{ - x + 6}{( \sqrt{2x + 4} + \sqrt{3x - 2}) ( - x + 6) } [/tex]
    [tex] = - \frac{1}{ \sqrt{2x + 4} + \sqrt{3x - 2} } [/tex]
    [tex] = - \frac{1}{ \sqrt{2 \times 6 + 4} + \sqrt{3\times 6 - 2} } = - \frac{1}{8} [/tex]

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