$f(x) = \begin{cases} \frac{\log x}{x-1}, & \text{if } x \neq 1 \\ k, & \text{if } x=1 \end{cases}$ is continuous at $x=1$,then the value of $k$ is

If a real valued function $f(x) = \begin{cases} \frac{x^2+(a+3)x+(a+1)}{x+3} & x \neq -3 \\ -\frac{5}{2} & x = -3 \end{cases}$ is continuous at $x = -3$,then $\lim_{x \rightarrow a} (x^2+x+1) = $

If the function $f(x) = \begin{cases} \frac{\cos ax - \cos bx}{\cos cx - \cos bx} & , x \neq 0 \\ -1 & , x = 0 \end{cases}$ is continuous at $x = 0$,then $a^2, b^2, c^2$ are in

If $f(x) = \begin{cases} \frac{x^2}{a} - a, & x < a \\ 0, & x = a \\ a - \frac{x^2}{a}, & x > a \end{cases}$ then:

If a real valued function $f(x) = \begin{cases} \log(1+[x]), & x \geq 0 \\ \sin^{-1}[x], & -1 \leq x < 0 \\ k([x]+|x|), & x < -1 \end{cases}$ is continuous at $x = -1$,then $k =$

If a real valued function $f(x) = \begin{cases} (1+\sin x)^{\operatorname{cosec} x}, & -\pi/2 < x < 0 \\ a, & x=0 \\ \frac{e^{2/x}+e^{3/x}}{a e^{2/x}+b e^{3/x}}, & 0 < x < \pi/2 \end{cases}$ is continuous at $x=0$,then $ab=$