Function $f\left(x\right)=\left\{\begin{array}{l}\begin{array}{cc}x-1;& x<2\end{array}\\ \begin{array}{cc}2x-3;& x\ge 2\end{array}\end{array}\right.$ is a continuous function

If a function $f\left(x\right)$ is defined as $f\left(x\right)=\left\{\begin{array}{c}\frac{x}{\sqrt{x^2}},x\ne 0\\ 0,x=0\end{array}\right.$, then

The value of $\lambda ,$ for which the function $f\left(x\right)=\left\{\begin{array}{cl}\lambda \left(x^2-2x\right)& \text{ if }x\le 0\\ 4x+1& \text{ if }x>0\end{array}\right.$ is continuous at $x=0,$ is

Let $f\left(x\right)=\left\{\begin{array}{lll}\frac{\sin (a+1)x+\sin x}{x}& ,& x<0\\ c& ,& x=0\\ \frac{\sqrt{x+b{x}^2}-\sqrt{x}}{b{x}^{3/2}}& ,& x>0\end{array}\right.$

If $f\left(x\right)$ is continuous at $x=0$, then