For every $r\in(0,+\infty)$, we define $f^r:\mathbb R\to\mathbb R$ to be
$f^r(x)=\begin{cases}\sqrt{r^2-x^2}&\text{if } |x|\leq r\\ 0 & \text{otherwise} \end{cases}$
a)Find all $p\geq 1$ such that the map $r\to f^r$ from $(0,+\infty)$ to $L^p(\mathbb R)$ is continuous
b)Find all $p\geq 1$ such that the map $r\to f^r$ from $(0,+\infty)$ to $L^p(\mathbb R)$ is differentiable
-Mario-
Edit
sorry everybody... i miscopied the text... i edited.. really i apologize..