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01 Учёба/1 семестр/Высшая математика/Контрольная.md
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### 1 (40 минут)
#учеба #семестр_1 #высшая_математика
#семестр_1 #высшая_математика
$\lim_{ x \to 3 } \frac{\sqrt{ x+13 }-2\sqrt{ x+1 }}{x^2-4x+3}$
$\frac{\sqrt{ x+13 }-2\sqrt{ x+1 }}{x^2-4x+3}=\frac{\sqrt{ x+13 }-2\sqrt{ x+1 }}{(x-1)(x-3)}\cdot \frac{\sqrt{ x+13 }+2\sqrt{ x+1 }}{\sqrt{ x+13 }+2\sqrt{ x+1 }}=\frac{\sqrt{ x+13 }^2-(2\sqrt{ x+1 })^2}{(x-1)(x-3)(\sqrt{ x+13 }+2\sqrt{ x+1 })}=\frac{(x+13)-4(x+1)}{(x-1)(x-3)(\sqrt{ x+13 }+2\sqrt{ x+1 })}=$