(a) If $f(x) = \begin{cases} x^2, & \text{if } x \geq 1 \\ x, & \text{if } x < 1 \end{cases}$, then show that $f$ is not differentiable at $x=1$. OR (b) Find the value(s) of '$\lambda$', if the function $f(x) = \begin{cases} \frac{\sin^2 \lambda x}{x^2} & \text{if } x \neq 0 \\ 1 & \text{if } x=0 \end{cases}$ is continuous at $x=0$.

Find whether the function $f(x)=\begin{cases}x-1, & x

If \(f(x)=\{[x],x\in R\}\) is the greatest integer function, then the correct statement is:

The function f defined by \(f(x)=\begin{cases}x,&if~x\le1\\ 5,&if~x>1\end{cases}\) is not continuous at:

Check the differentiability of f(x) at $x=-2$ if $f(x)=\begin{cases}2x-3,-3\le x\le-2\\ x+1,-2