Looking for a multivariable function with an assymptote and a gradient bounded away from zero.

Question

I am Looking for a multivariable function with an assymptote and a gradient bounded away from zero.

For example: let $f:\mathbb{R}^k\rightarrow\mathbb{R}$ be a function such that

1. $lim f(x_1,\cdots x_k)\rightarrow M$ where $M$ is a finite constant
2. $\forall x\in \mathbb{R}^k$, $\nabla f>\delta(x)$ where $\delta(x)>0$.