List of top Mathematics Questions on Limit and Continuity asked in CBSE CLASS XII

If \[ f(x)= \begin{cases} \dfrac{x^2-4x-5}{x+1}, & x\neq-1,\\[6pt] k, & x=-1, \end{cases} \] is continuous at \(x=-1\), then the value of \(k\) is:

If $f(x) = 3x - b$, $x>1$ ; $f(x) = 11$, $x = 1$ ; $f(x) = -3x - 2b$, $x<1$ is continuous at $x = 1$, then the values of $a$ and $b$ are :
If \( f(x) = \begin{cases} \frac{\sin^2 ax}{x^2}, & \text{if } x \neq 0 \\ 1, & \text{if } x = 0 \end{cases} \) is continuous at \( x = 0 \), then the value of 'a' is :