Let f(x) be defined as follows

$$f(x) = \left\{ {\matrix{ {2x + 1,} & { - 3 < x < - 2} \cr {x - 1,} & { - 2 \le x < 0} \cr {x + 2,} & {0 \le x < 1} \cr } } \right.$$

Which one of the following statements is correct in respect of the above function?

Consider the following statements

1. If $$\mathop {\lim }\limits_{x \to a} f(x)$$ and $$\mathop {\lim }\limits_{x \to a} g(x)$$ both exist, then $$\mathop {\lim }\limits_{x \to a} \{ f(x)g(x)\} $$ exists.

2. If $$\mathop {\lim }\limits_{x \to a} \{ f(x)g(x)\} $$ exists, then both $$\mathop {\lim }\limits_{x \to a} f(x)$$ and $$\mathop {\lim }\limits_{x \to a} g(x)$$ must exist.

Which of the above statement is/are correct?

Consider the function $$f(x) = \left\{ {\matrix{ {{{\sin 2x} \over {5x}},} & {if\,x \ne 0} \cr {{2 \over {15}},} & {if\,x = 0} \cr } } \right.$$

Which one of the following is correct in respect of the function?

For the function f(x) = | x $$-$$ 3 |, which one of the following is not correct?