List of top Mathematics Questions on Continuity of a function asked in CBSE Class XII

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

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

Show that the function \( f(x) = \begin{cases \frac{\cos x}{\frac{\pi}{2}-x}, & x \neq \frac{\pi}{2} \\ 1, & x = \frac{\pi}{2} \end{cases} \) is continuous at \( x = \frac{\pi}{2} \).}
If \(f(x) = \begin{cases \frac{\sin x}{x} + \cos x, & x \neq 0 \\ k, & x = 0 \end{cases}\) is continuous at \(x = 0\), then the value of \(k\) is :}
The value of \(k\) for which the function \(f(x) = \begin{cases x^2 \sin \frac{1}{x}, & x \neq 0 \\ k(x + 1), & x = 0 \end{cases}\) is a continuous function, is :}
Check whether function \( f(x) \) defined as \( f(x) = \begin{cases \frac{|x - 3|}{2(x - 3)} & , x \\ \frac{x - 6}{6} & , x \geq 3 \end{cases} \) is continuous at \( x = 3 \) or not ?}