Let $\rm f(x) = \left\{\begin{matrix} 1+\frac{x}{2k}, & 0 < x < 2\\\ kx, & 2 \le x < 4 \end {matrix}\right.$

If $\displaystyle\lim_{x\rightarrow 2}$ f(x) exists, then what is the value of k?

Consider the following statements in respect of f(x) = |x| - 1

1. f(x) is continuous at x = 1.

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

Which of the above statements is/are correct?

If $f(x) = \frac{[x]}{|x|}$, x ≠ 0, where [⋅] denotes the greatest integer function, then what is the right-hand limit of f(x) at x = 1?

Consider the following statements in respect of the function $\rm f(x) = sin \left(\frac{1}{x^2}\right)$, x ≠ 0:

1. It is continuous at x = 0, if f(0) = 0.

2. It is continuous at $x = \frac{2}{\sqrt{\pi}}$.

Which of the above statements is/are correct?