List of top Mathematics Questions on Continuity of a function asked in CUET (UG)

Is \[ f(x)=x^2 \] continuous at \(x=0\)?

If the function \( f(x) \) defined below is continuous at \( x = 2 \), find the value of the constant \( k \): \[ f(x) = \begin{cases} kx^2 & \text{if } x \le 2 3x - 2 & \text{if } x > 2 \end{cases} \]