# Problem of limit or limit of problem

Calculus Level 5

You are given the curve $$\sin(x) + \sin(y) = 1$$ lying in the first quadrant. Given that for some constant $$\alpha$$, the limit $$\displaystyle \lim_{x\to0} x^\alpha \dfrac{d^2 y}{dx^2}$$ exists and is non-zero. Find $$2\alpha$$.

This problem is part of Math's Planet

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