Limit

Calculus Level 2

limx21+2+x3x2 \lim_{x\to2} \dfrac{\sqrt{1+\sqrt{2+x}} - \sqrt3}{x-2}

If the value of the limit above is equal to 1ab \dfrac 1{a\sqrt b} , where aa and bb are integers with bb square-free, find 2016a×b\dfrac{2016}{a\times b} .

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