If $f(x) = \begin{cases} \log(\sec^2 x)^{\cot^2 x}, & x \neq 0 \\ K, & x = 0 \end{cases}$ is continuous at $x = 0$,then $K$ is

Which of the following statements is true for the graph of the function $f(x) = \log x$?

Let $f(x) = \begin{cases} x^p \sin \left( \frac{1}{x} \right) + x|x^3|, & x \neq 0 \\ 0, & x = 0 \end{cases}$. Then the complete set of values of $p$ for which $f''(x)$ is continuous at $x = 0$ is:

Let $f(x) = x^2 + x \sin x - \cos x$. Then

If $f(x) = \begin{cases} x^2, & \text{when } x \le 1 \\ x + 5, & \text{when } x > 1 \end{cases}$,then

Let $f:[-1,2] \rightarrow \mathbb{R}$ be given by $f(x)=2x^2+x+[x^2]-[x]$,where $[t]$ denotes the greatest integer less than or equal to $t$. The number of points where $f$ is not continuous is: