Continuity of a function with real paramter Let $f:\mathbb{R^3}$ $\rightarrow$ $\mathbb{R}$,  defined as: 
$$f(x,y,z)=\begin{cases} \left(x^2+y^2+z^2\right)^p \exp\left(\frac{1}{\sqrt{x^2+y^2+z^2}}\right)& ,\,\text{if }\quad(x,y,z) \ne (0,0,0)\quad \\
 0 &,\,\text{o.w}
\end{cases}$$
Where $\,p\in \mathbb{R}$. Is this function is continuous?

Using the well-known limit
$$\forall p\in \mathbb R\;\;\lim_{X\to +\infty}\frac{e^X}{X^p}=+\infty$$ 
we get
$$\lim_{x\to 0}f(x,0,0)=+\infty$$
thus, the function is not continuous at $0$ but it is at $\mathbb R\setminus \{0\}$.
