(Solved): 1) Bent Vector Calc (20 points) a) Using cylindrical coordinates, calculate \[ \vec{\nabla} \mathr ...

1) Bent Vector Calc (20 points) a) Using cylindrical coordinates, calculate \[ \vec{\nabla} \mathrm{e}^{-\rho^{2}} \] b) For the function given in cylindrical coordinates as \[ f(\vec{r})=\mathrm{e}^{-\left(\rho^{2}+z^{2}\right)} \] calculate the definite integral over the volume of all space. You can work in whatever coordinates you like. Feel free to give your answer with a form of the Gamma function if you want. (Forms are on the front page.)