For the function $f(x)=|\cos x|$, which of the following statements are correct?

(A) $f(x)$ is continuous for all $x \in \mathbb{R}$

(B) $f(x)$ is differentiable for all $x \in \mathbb{R}$

(C) $f(x)$ is not differentiable at $x=(2n+1)\dfrac{\pi}{2}, n \in \mathbb{Z}$

(D) $f(x)$ is not differentiable at $x=n\pi, n \in \mathbb{Z}$

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If the function $f(x)=\begin{cases} x^2, & x\le c \\ ax+b, & x>c \end{cases}$ is differentiable at $x=c$, then the relation between $b$ and $c$ is:

If $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots + \infty}}}$ then $\frac{dy}{dx}$ equals to

If $e^y(x+1)=1$, then

The function $f(x)=\begin{cases}\frac{e^{3x}-e^{-5x}}{x}, & x\neq 0\\ \lambda, & x=0\end{cases}$ is continuous at x=0 for the value of '$\lambda$' as:

If $y = \sin^{-1}x$, then $(1-x^2)\frac{d^2y}{dx^2}$ is equal to

For the function $f: \mathbb{R} \to \mathbb{R}$ given by $f(x) = \lvert x-3 \rvert + \lvert x+4 \rvert$, Where $\mathbb{R}$ is set of real numbers, which of the following statements are correct?

(A) $f(x)$ is continuous as well as differentiable at $x=3$.

(B) $f(x)$ is continuous but not differentiable at $x=3$ and $x=-4$

(C) $f(x)$ is neither continuous nor differentiable at $x=3$

(D) $f(x)$ is continuous on $\mathbb{R}$

Choose the correct answer from the options given below: