lim x mendekati tak hingga√2x+1 - √3x -2

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Jawaban

  • Jawaban diposting oleh: supaat69
    [tex]\begin{aligned}&\lim_{x\rightarrow\infty}\left(\sqrt{2x+1}-\sqrt{3x-2}\right)\cdot\frac{\sqrt{2x+1}+\sqrt{3x-2}}{\sqrt{2x+1}+\sqrt{3x-2}}\\=&\lim_{x\rightarrow\infty}\frac{\sqrt{2x+1}^2-\sqrt{3x-2}^2}{\sqrt{2x+1}+\sqrt{3x-2}}\\=&\lim_{x\rightarrow\infty}\frac{2x+1-3x+2}{\sqrt{2x+1}+\sqrt{3x-2}}\\=&\lim_{x\rightarrow\infty}\frac{-x+3}{\sqrt{2x+1}+\sqrt{3x-2}}\cdot\frac{\frac{1}{x}}{\frac{1}{\sqrt{x^2}}}\\=&\lim_{x\rightarrow\infty}\frac{-1+\frac{3}{x}}{\sqrt{\frac{2}{x}+\frac{1}{x^2}}+\sqrt{\frac{3}{x}-\frac{2}{x^2}}}\\=&\infty\end{aligned}[/tex]

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lim x mendekati tak hingga√2x+1 - √3x -2

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