1.
Let [x][x] denote the greatest integer less than or equal to xx. Then
limx0tan(πsin2x)+(xsin(x[x]))2x2\lim_{x \to 0} \frac{\tan\left(\pi\sin^2 x\right) + \left(|x|-\sin\left(x[x]\right)\right)^2}{x^2}