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

If \(y=e^{4x}(92)^x\); then \(\frac{dy}{dx}\) is equal to
(\(\log_e x=\log x\))

Function \(f(x)=\begin{cases} k\left(x^2-6x+13\right) & : x<1 \\ |x-3| & : x\ge 1 \end{cases}\) is differentiable at \(x=1\), then the value of \(k\) is

If \(x=\sec\theta+\cos\theta,\ y=\sec^n\theta+\cos^n\theta\), then \(\frac{dy}{dx}\) is equal to

If \(y = \sqrt{\dfrac{1-x}{1+x}}\), then the value of \((1 - x^2)\dfrac{dy}{dx} + y\) is

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