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This is a case where we can apply l'Hopital's rule, separately calculating the derivatives of the numerator and denominator, then take the limit using those:

Limx→2 [(6 - x)1/2 - 2] / [(3 - x)1/2 - 1]

= Limx→2 [1/2(6 - x)-1/2 (-1)] / [1/2(3 - x)-1/2 (-1)]

= Limx→2 (3 - x)1/2 / (6 - x)1/2

= 1/2

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13y ago

What else can I help you with?