If $f(x) = \begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, & \text{for } -1 \leq x < 0 \\ 2x^2+3x-2, & \text{for } 0 \leq x \leq 1 \end{cases}$ is continuous at $x=0$,then $k$ is equal to

Let $f(x) = \frac{1 - x(1 + |1 - x|)}{|1 - x|} \cos \left(\frac{1}{1 - x}\right)$ for $x \neq 1$. Then

If $f: R \rightarrow R$ is a function defined by $f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi,$ where $[.]$ denotes the greatest integer function,then $f$ is

If $f(x) = \begin{cases} \frac{1-\cos Kx}{x \sin x}, & \text{if } x \neq 0 \\ \frac{1}{2}, & \text{if } x=0 \end{cases}$ is continuous at $x=0$,then the value of $K$ is

Let $f(x) = \begin{cases} \frac{\sin \pi x}{5x}, & x \ne 0 \\ k, & x = 0 \end{cases}$. If $f(x)$ is continuous at $x = 0$,then $k =$

If $a$ and $b$ $(a > b)$ are points of discontinuity of the function $f(x) = \begin{cases} 3-2x^2, & \text{for } x \leq 0 \\ 2x+3, & \text{for } 0 < x \leq 1 \\ 2x^2-3x, & \text{for } 1 < x < 2 \\ 2x-3, & \text{for } 2 \leq x < 3 \\ |x|, & \text{for } x \geq 3 \end{cases}$,then $3a-b = $