List of top Mathematics Questions on Limit and Continuity asked in UP Board XII

If \( f(x) = \begin{cases} -2 & \text{if } x \le -1 \\ 2x & \text{if } -1 < x \le 1 \\ 2 & \text{if } x > 1 \end{cases} \), then test the continuity of the function at \( x = -1 \) and at \( x = 1 \).
Does the function \( f(x) = \begin{cases} x+5 & \text{if } x \le 1 \\ x-5 & \text{if } x > 1 \end{cases} \) continuous at \( x = 1 \)?
Show that \( f(x) = |x| \) is continuous for all values of x.
Prove that the function f(x) = |x| is continuous at x = 0.