\lim \frac{(1 + x^{2} ) \cdot (e^{1.5x^2} - 1 ) \cdot \frac {x}{2}}{ 3x\cdot \frac{x}{2} } - \lim \frac{ x^2}{3x}= \lim (1 + x^{2} ) \cdot \frac {x}{2} - \lim \frac{x}{3}=0 ?