1.
If α=limx0x2xx1cosx\alpha=\displaystyle\lim_{x\to0}\frac{x\cdot2^x-x}{1-\cos x} and β=limx0x2xx1+x21x2\beta=\displaystyle\lim_{x\to0}\frac{x\cdot2^x-x}{\sqrt{1+x^2}-\sqrt{1-x^2}}, then