\displaystyle\lim_{x\to 0} \frac{(1 + x^{2} ) \cdot e^{1.5x^2} - 1}{x \cdot \sin2x }= \displaystyle\lim_{x\to 0} \frac{(1 + x^{2} ) \cdot e^{1.5x^2} - 1 - x^2 + x^2}{ \frac{ \sin2x }{2x}\cdot 2x^2 }=