If $f(x) = \begin{cases} x^2 - 1, & \text{if } x \ge 2 \\ x + 1, & \text{if } x < 2 \end{cases}$, then $\lim_{x \to 1} f(x) + \lim_{x \to 2} f(x) =$

The function $f(x) = \sin |x|$ is

If $f(x) = \begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x} & ; -1 \leq x < 0 \\ \frac{2x+1}{x-1} & ; 0 \leq x \leq 1 \end{cases}$ is continuous at $x=0$,then the value of $k$ is:

$f(x) = \begin{cases} \frac{1-\cos kx}{x^2}, & x \le 0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & x > 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is:

If the function $f(x) = \frac{1 - \cos 4x}{8x^2}$ for $x \ne 0$ and $f(x) = k$ for $x = 0$ is a continuous function at $x = 0$,then the value of $k$ is:

If $f(x) = \begin{cases} \frac{\sin x}{x} + \cos x, & x \ne 0 \\ 2, & x = 0 \end{cases}$,then which of the following is true?