If the function $f(x) = \begin{cases} \frac{k\cos x}{\pi - 2x} & : x \neq \frac{\pi}{2} \\ 3 & : x = \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}$, then $k$ is equal to

Let $y = \cos(\sin x^2)$, then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{\pi}}{2}$ is equal to

For the function $f(x) = |x + 1| + |x - 1| + |x - 2|$ which of the following are TRUE?

A. $f(x)$ is continous on $\mathbb{R}$

B. $f(x)$ is not differentiable at $x = 1$

C. $f(x)$ is differentiable on $\mathbb{R}$

D. $f(x)$ has no local maxima

Choose the correct answer from the options given below:

Let $f(x)=\begin{cases}\dfrac{|x|}{x},&x\ne0\\1,&x=0\end{cases}$ and $g(x)=\begin{cases}x\sin\left(\dfrac{1}{x}\right),&x\ne0\\0,&x=0\end{cases}$

Then at the origin, which one of the following is true?

The equation of the tangent to the curve $\mathrm{x}^{\frac{5}{2}}+\mathrm{y}^{\frac{5}{2}}=33$ at the point $(1,4)$ is :

If $e^y(1+x)=1$, then $\dfrac{d^2y}{dx^2}$ is:

If $y=\frac{\log x}{x}$, then $\frac{d^2y}{dx^2}$ is equal to(Consider $\log_e x = \log x$):