For the function $f(x) = \sqrt{x}$, which of the following statements are true?

(A) $f(x)$ is continuous for $x \geq 0$.

(B) $f(x)$ is continuous for $x \in R$ (Set of real numbers).

(C) $f(x)$ is differentiable for $x > 0$.

(D) $f(x)$ is differentiable for $x \in R$ (Set of real numbers).

Choose the correct answer from the options given below:

Match List-I with List-II

Where $\mathbb{R}$ is set of real numbers

Choose the correct answer from the options given below:

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If the function $f(x)=\begin{cases}\frac{1-\cos kx}{\sin^2 x}, & x\ne0\\\frac{1}{2}, & x=0\end{cases}$ is continuous at $x=0$, then the value of $k$ is