1. $\displaystyle \lim_{x \rightarrow +\infty} \dfrac{sin(x)}{x+1}=$

2. $\displaystyle \lim_{x \rightarrow -\infty} cos\left(\dfrac{x}{x^2+2}\right)=$

3. $\displaystyle \lim_{x \rightarrow +\infty} 3x^2-xcos(x)=$

4. $\displaystyle \lim_{x \rightarrow +\infty} e^{-x^2+1}=$

5. $\displaystyle \lim_{x \rightarrow -\infty} (x+3)e^{x+3} =$