List of top Mathematics Questions on Continuity asked in VITEEE

Let \( f \) be the function defined by \[ f(x) = \begin{cases} x^2 - 1, & x \neq 1 \\ x^2 - 2|x-1|^{-1}, & x = 1 \end{cases} \] The function is continuous at:

At how many points between the interval \( (-\infty, \infty) \) is the function \( f(x) = \sin x \) is not differentiable?

\( f(x) = \left\{ \begin{array}{ll} \sin \frac{1}{x} , & \text{for} \, x \neq 0 \\ 0, & \text{for} \, x = 0 \end{array} \right. \) is:

The number of points of discontinuity of the function \( f(x) = x - [x] \) in the interval \( (0, 7) \) are:

The set of points of discontinuity of the function \[ f(x) = \sin (2 \sin x) \sin^2 x \] is given by

If \( f(x) = \left\{ \begin{array}{ll} 1 + \left| \sin x \right|, & \text{for } -\pi \leq x<0
e^{x/2}, & \text{for } 0 \leq x<\pi
\end{array} \right. \) then the value of \( a \) and \( b \), if \( f \) is continuous at \( x = 0 \), are respectively

If \( f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{for } x \leq \frac{\pi}{2}, \\ \sin x + n, & \text{for } x>\frac{\pi}{2}, \end{array} \right. \) is continuous at \( x = \frac{\pi}{2} \), then:

If \( f(x) = \frac{x^2}{2}, \text{for} x \leq 0, \frac{2\sin x}{x}, \text{for} x>0 \), then \( x = 0 \) is:

Let [ ] denote the greatest integer function and f (x) = [tan$^2$ x]. Then