If the function $f$ is continuous at $x = \pi$, where $f(x) = \frac{1 - \cos[7(x - \pi)]}{5(x - \pi)^2}$ for $x \neq \pi$, then $f(\pi) =$

If $f(x) = \begin{cases} \frac{a \sin x - b x + c x^2 + x^3}{2 \log(1+x) - 2x + x^2 - \frac{2}{3}x^3} &, x \neq 0 \\ 0 &, x=0 \end{cases}$ is continuous at $x=0$,then find the relation between $a, b, c$.

The values of $p$ and $q$ for which the function $f(x) = \begin{cases} \frac{\sin(p+1)x + \sin x}{x} & x < 0 \\ q & x = 0 \\ \frac{\sqrt{x+x^2} - \sqrt{x}}{x^{3/2}} & x > 0 \end{cases}$ is continuous for $\forall x \in R$ are

If the function defined by $f(x) = \begin{cases} (x^2 + e^{\frac{1}{2-x}})^{-1}, & x \neq 2 \\ k, & x = 2 \end{cases}$ is right continuous at $x = 2$, then $k =$

Let $f(x) = \begin{cases} |x|, & -\infty < x < 2 \\ |2x-4|, & 2 \leq x \leq 20 \end{cases}$. If $x=a$ is a point where $f(x)$ is continuous but not differentiable and $x=b$ is a point where $f(x)$ is not differentiable $(a \neq b)$,then $a+b=$

The function $f(x) = \begin{cases} \frac{x - |x|}{x}, & x \neq 0 \\ 2, & x = 0 \end{cases}$