If $f(x) = \frac{\ln(e^{x^2} + 2\sqrt{x})}{\sqrt{x}}$ is continuous at $x = 0$,then $f(0)$ must be equal to:

If the function $f(x) = \left( \frac{5x - 8}{8 - 3x} \right)^{\frac{3}{2x-4}}$ for $x \neq 2$ is continuous at $x = 2$, then the value of $f(2)$ is...

If $f: R \rightarrow R$ defined as $f(x) = \frac{x^3+2x^2+x+2}{x^2+x-2}$ (when $x \neq -2$) is continuous at $x = -2$, then $f(-2)$ is equal to

Let $[t]$ denote the greatest integer $\leq t$. The number of points where the function $f(x)=[x]|x^{2}-1|+\sin \left(\frac{\pi}{[x]+3}\right)-[x+1]$ for $x \in(-2,2)$ is not continuous is:

The number of points where the function $f(x) = \begin{cases} |2x^2 - 3x - 7| & \text{if } x \leq -1 \\ [4x^2 - 1] & \text{if } -1 < x < 1 \\ |x+1| + |x-2| & \text{if } x \geq 1 \end{cases}$ is discontinuous,where $[t]$ denotes the greatest integer $\leq t$,is:

Let $f(x) = x \cdot \left[ \frac{x}{2} \right]$ for $-10 < x < 10$,where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to