Consider the following for the next two (02) items that follow:

Let $f(x) = |x| + 1$ and $g(x) = [x] - 1$, where [.] is the greatest integer function.

Let $h(x) = \frac{f(x)}{g(x)}$.

Consider the following statements:

1. $f(x)$ is differentiable for all $x < 0$

2. $g(x)$ is continuous at $x = 0.0001$

3. The derivative of $g(x)$ at $x = 2.5$ is 1

Which of the statements given above are correct?

Consider the following for the next two (02) items that follow:

Let $f(x) = |x| + 1$ and $g(x) = [x] - 1$, where [.] is the greatest integer function.

Let $h(x) = \frac{f(x)}{g(x)}$.

What is $\lim\limits_{x \to 0-} h(x) + \lim\limits_{x \to 0+} h(x)$ equal to?

Consider the following for the next two (02) items that follow:

Let $\varphi(a) = \int_{a}^{a + 100 \pi} |\sin x| dx$

What is $\varphi(a)$ equal to?

Consider the following for the next two (02) items that follow:

Let $\varphi(a) = \int_{a}^{a + 100 \pi} |\sin x| dx$

What is $\varphi'(a)$ equal to?