Let $$f(x) = \left\{ {\matrix{ {{{{e^x} - 1} \over x},} & {x > 0} \cr {0,} & {x = 0} \cr } } \right.$$, be a real valued function, then which of the following statements is/are correct?

I. f(x) is right continuous at x = 0

II. f(x) is discontinuous at x = 1

Select the correct answer using the code given below.

Consider the equation x + | y | = 2y.

Which of the following statements are not correct?

1. y as a function of x is not defined for all real x.

2. y as a function of x is not continuous at x = 0.

3. y as a function of x is differentiable for all x.

Select the correct answer using the codes given below.

Consider the equation x + | y | = 2y.

What is the derivative of y as a function of x with respect to x for x < 0 ?

Consider the equation $$f(x) = {{{a^{[x] + x}} - 1} \over {[x] + x}}$$ where [ . ] denotes the greatest integer function.

What is $$\mathop {\lim }\limits_{x \to {0^ + }} f(x)$$ equal to