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بِسْـــمِ اللَّهِ الرَّحْمَــنِ الرَّحِيْمِ
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[tex]\displaystyle\sf\lim_{x \to \infty} \: (x + 5) - \sqrt{ {x}^{2} + 4x - 3} [/tex]
[tex]\displaystyle\sf\lim_{x \to \infty} \: \sqrt{ {(x + 5)}^{2} } - \sqrt{ {x}^{2} + 4x - 3}[/tex]
[tex]\displaystyle\sf\lim_{x \to \infty} \: \sqrt{ {x}^{2} + 10x + 25} - \sqrt{ {x}^{2} + 4x - 3} [/tex]
[tex]\displaystyle\sf \: \: \: \: \: \: \: = \frac{10 - 4}{2 \sqrt{1} } [/tex]
[tex]\displaystyle\sf \: \: \: \: \: \: \: = \frac{6}{2 \times 1} [/tex]
[tex]\displaystyle\sf \: \: \: \: \: \: \: = \frac{6}{2} [/tex]
[tex]\displaystyle\sf \: \: \: \: \: \: \: = 3[/tex]
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وَاللَّهُ عَالَمُ بِاالصَّوَافَ
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