Consider a function $f:(0,1) \rightarrow\{0,1\}$ defined as follows.

For a real number $r \in(0,1), f(r)=1$ if the second digit after the decimal point in $r$ is one of the four digits $2,3,6$ and 7 . Otherwise, $f(r)$ is equal to 0 .

The number of points in $(0,1)$ at which $f$ is discontinuous is $\_\_\_\_$ . (answer in integer)

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as follows:

$$ f(x)=\left(\frac{|x|}{2}-x\right)\left(x-\frac{|x|}{2}\right) $$

Which of the following statements is/are true?

The value of $$\int_0^{\pi /4} {x\cos \left( {{x^2}} \right)dx} $$ correct to three decimal places (assuming that $$\pi = 3.14$$ ) is ________.

The value of $$\mathop {\lim }\limits_{x \to 1} {{{x^7} - 2{x^5} + 1} \over {{x^3} - 3{x^2} + 2}}.$$