The value of $f(4)-f(3)$ is

Which one of the following statements is $NOT \text{ } CORRECT$?

Match the functions in Column $I$ with their properties in Column $II$. In the following $[x]$ denotes the greatest integer less than or equal to $x$.

Column $I$	Column $II$
$A$. $x|x|$	$I$. Strictly increasing and continuous in $(-1,1)$
$B$. $\sqrt{|x|}$	$II$. Continuous but not differentiable in $(-1,1)$
$C$. $x+[x]$	$III$. Differentiable in $(-1,1)$
$D$. $|x-1|+|x+1|+|x|$	$IV$. Differentiable in $(-1,0) \cup (0,1)$
	$V$. Strictly increasing and not differentiable in $(-1,1)$

The correct match is

Consider $f(x) = \begin{cases} \tan^{-1}(\frac{\alpha x + \beta}{\gamma}) & x \in (0, \frac{1}{2}) \\ 0 & x = \frac{1}{2} \\ \ln(\beta x^2 + 2) & x \in (\frac{1}{2}, 1) \end{cases}$. If $f(x)$ is continuous and differentiable in its domain,then the value of $\alpha + \beta + \gamma$ is:

Let $f(x) = \begin{cases} \frac{1}{|x|}, & |x| \geqslant 1 \\ ax^2 + b, & |x| < 1 \end{cases}$ be continuous and differentiable everywhere. Then $a$ and $b$ are

$\mathop {Lim}\limits_{\lambda \to 0} \,{\left( {\int\limits_0^1 {{{(1 + x)}^\lambda }dx} } \right)^{\frac{1}{\lambda }}}$ is equal to