Limieten van vierkantswortels

$\eqalign{ & \mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {x + 6} - \sqrt {3x} }} {{\sqrt {x - 3} }} = \cr & \mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {x + 6} - \sqrt {3x} }} {{\sqrt {x - 3} }} \cdot \frac{{\sqrt {x + 6} + \sqrt {3x} }} {{\sqrt {x + 6} + \sqrt {3x} }} = \cr & \mathop {\lim }\limits_{x \to 3} \frac{{x + 6 - 3x}} {{\sqrt {x - 3} \cdot \left( {\sqrt {x + 6} + \sqrt {3x} } \right)}} = \cr & \mathop {\lim }\limits_{x \to 3} \frac{{ - 2x + 6}} {{\sqrt {x - 3} \cdot \left( {\sqrt {x + 6} + \sqrt {3x} } \right)}} = \cr & \mathop {\lim }\limits_{x \to 3} \frac{{ - 2\left( {x - 3} \right)}} {{\sqrt {x - 3} \cdot \left( {\sqrt {x + 6} + \sqrt {3x} } \right)}} = \cr & \mathop {\lim }\limits_{x \to 3} \frac{{ - 2\sqrt {x - 3} }} {{\sqrt {x + 6} + \sqrt {3x} }} = \frac{{ - 2\sqrt {3 - 3} }} {{\sqrt {3 + 6} + \sqrt {3 \cdot 3} }} = 0 \cr}$

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• Limieten van vierkantswortels