Consider the following in respect of the function

$$f(x) = \left\{ \matrix{ 2 + x,x \ge 0 \hfill \cr 2 - x,x < 0 \hfill \cr} \right.$$.

I. $$\mathop {\lim }\limits_{x \to 1} f(x)$$ does not exist.

II. f(x) is differentiable at x = 0.

III. f(x) is continuous at x = 0.

Which of the above statements is/are correct?

Let f : A $$\to$$ R, where A = R \ {0} is such that $$f(x) = {{x + |x|} \over x}$$. On which one of the following sets is f(x) continuous?

Let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R.

Which of the following statements is correct?

Let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R.

Which one of the following statements is correct?