\lim \frac{(1 + x^{2} ) \cdot e^{1.5x^2} - 1}{x \cdot \sin2x }= \lim \frac{(1 + x^{2} ) \cdot e^{1.5x^2} - 1}{ \frac{x \cdot \sin2x \cdot2x}{2x} }= \lim \frac{(1 + x^{2} ) \cdot e^{1.5x^2} - 1 + x^2 - x^2}{ \frac{ \sin2x \cdot3x}{2x} }=