$f(x)= \begin{cases}(1+3x)^{\frac{4}{x}}, & \text{if } x \neq 0 \\ a, & \text{if } x=0 \end{cases}$
If $f$ is continuous at $x=0$,then $\log a=$

Show that the function defined by $f(x)=\cos \left(x^{2}\right)$ is a continuous function.

At $x=0$,the function $f(x) = \begin{cases} \frac{x}{|x|+2x^2}, & x \neq 0 \\ k, & x=0 \end{cases}$ is:

If $f: [-2, 2] \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\sqrt{1 + cx} - \sqrt{1 - cx}}{x}, & -2 \leq x < 0 \\ \frac{x + 3}{x + 1}, & 0 \leq x \leq 2 \end{cases}$ is continuous on $[-2, 2]$,then $c$ is equal to

If $f(x) = \begin{cases} e^{1/x}, & x \ne 0 \\ 0, & x = 0 \end{cases}$,then:

If $f:(-7,7) \rightarrow R$ is defined by $f(x)=[x]$ for all $x \in (-7,7)$,then the number of discontinuities of $f$ is