Consider the following for the next items that follow:

Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$

If the function f(x) is differentiable at x = 1, then what is the value of (a + b)?

Consider the following for the next items that follow:

Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$

What is $\displaystyle \lim _{x \rightarrow 0} $ f(x) equal to ?

Consider the following for the next three (03) items that follow :

Let f(x) = $\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1 \end{array}\right|$

What is $\lim _{x \rightarrow 0} \frac{f(x)}{x}$ equal to ? 

Consider the following for the next three (03) items that follow :

Let f(x) = $\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1 \end{array}\right|$

What is $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}$ equal to ?